OBI 
355 


UC-NRLF 


YFQ2600 


TABLES 


FOR  THE 


TRUE  ANOMALY 


IN   ELLIPTIC  ORBITS 


BY 


FRANK   SCHLESINGER  AND   STELLA    UDICK 


REPRINTED  FROM  THE  PUBLICATIONS  OF  THE  ALLEGHENY  OBSERVATORY,  VOLUME  II 


PRESS  OF 

THE  NEW  ERA  PRINTING  COMPANY 
LANCASTER,  PA. 

1912 


S4 

.•-uron.  D« 


TABLES  FOR  THE  TRUE  ANOMALY  IN  ELLIPTIC  ORBITS. 

BY   FRANK   SCHLESINGER  AND   STELLA   UDICK. 

The  following  tables  have  been  compiled  to  facilitate  the  computation  of  the 
orbits  of  spectroscopic  and  visual  binaries.  They  should  also  prove  useful  for 
the  computation  of  finding  ephemerides  for  asteroids. 

The  true  anomaly  (r)  of  a  body  moving  in  an  elliptic  orbit  is  the  angle  be- 
tween its  radius-vector  and  the  major  axis;  it  is  counted  from  periastron,  or  that 
end  of  the  axis  that  corresponds  to  closest  approach  to  the  attracting  body.  The 
mean  anomaly  (M)  is  what  this  angle  would  be  were  the  angular  motion  uni- 
form. These  two  anomalies  are  connected  by  the  equations: 

E—e  sin  E  =  ^f,  (i) 


(2) 


in  which  £  is  an  auxiliary  called  the  eccentric  anomaly.  As  the  first  of  these 
equations  is  transcendental,  the  task  of  computing  £  from  M  is  one  of  classic 
difficulty  and  is  known  as  Kepler's  problem.  Among  the  numerous  devices  that 
have  been  provided  for  the  solution  of  this  problem,  the  two  most  useful  are  the 
"  Tafel  zur  Berechnung  der  ivahre  Anomalie  "  published  by  the  Berlin  Rechen- 
Institut  in  1892,  and  Astrand's  "  Hiilfstafeln  zurAuflosung  der  Kepler  'schen  Prob- 
lems," Leipzig,  1890.  The  former  gives  the  values  of  v  —  M  to  the  hundredth 
part  of  a  minute  of  arc;  the  arguments  are  each  degree  in  M  and  each  20'  in  <£, 
up  to  20°  20',  0  being  the  angle  whose  sine  is  equal  to  the  eccentricity  of  the 
orbit.  Astrand's  tables  give  the  values  of  £  to  the  thousandth  part  of  a  degree; 
the  arguments  are  each  degree  in  M  and  each  hundredth  in  the  eccentricity  from 
o.oi  to  i.oo.  In  addition  each  half-degree  in  M  from  o°-5  to  19°.  5  is  included. 
Both  these  tables  were  designed  more  especially  with  a  view  to  facilitating  the 
computation  of  asteroid  orbits.  The  present  tables  give  the  values  of  v  directly, 
to  the  hundredth  part  of  a  degree,  the  arguments  being  each  degree  in  M  and 
each  hundredth  in  e  from  o.oi  to  0.77  inclusive.  Any  greater  accuracy  than 


FOR    THE    TRUE    ANOMALY. 

o°.oi  is  superfluous  for  either  spectroscopic  or  visual  binaries.  As  it  is  frequently 
necessary  to  interpolate  for  the  thousandths  in  the  eccentricity,  the  tables  have 
been  arranged  with  this  in  view,  and  successive  values  of  v  for  the  same  value 
of  M  (but  different  values  of  e)  are  found  in  the  same  horizontal  line. 

The  usefulness  of  tables  depends  so  largely  upon  their  freedom  from  error 
that  compilers  should  always  state  how  they  were  computed  and  what  precau- 
tions were  taken  to  insure  the  accuracy  of  their  printing.  In  the  present  case,  v 
has  been  computed  from  the  corresponding  £  in  Astrand's  tables  by  means  of 
Equation  (2)  above.  Bremiker's  five-place  logarithms  were  employed  and  the 
work  was  carried  out  to  three  decimal  places.  It  was  then  checked  in  the  fol- 
lowing way:  from  <?  =  o.oi  to  e  =  o.io,  v  was  computed  to  three  decimal  places 
from  the  formula, 

v  —  M+  2(E—  M}  +  ^  sin  zM+  $e?  sin  3^/+  etc. 


E  —  M  was  taken  from  Astrand's  tables.  This  expression  is  not  conveniently 
convergent  beyond  ?  =  o.io;  and  v  was  therefore  computed  in  duplicate  from 
^  =  o.ii  to  £  =  0.23.  Next,  by  means  of  the  second  differences  (and  the  third 
whenever  necessary)  the  computed  values  of  v  were  checked  throughout  the 
whole  extent  of  the  tables.  For  the  larger  values  of  e,  the  method  of  differences 
is  not  servicable  at  the  beginning  of  each  table,  and  these  values  of  v  were  accord- 
ingly checked  by  duplicate  computations.  The  tables  were  now  copied  on  sheets 
for  the  printer  and  were  rounded  off  to  two  decimal  places.  The  copying  was 
checked  by  taking  the  differences  upon  these  printer's  sheets,  that  is  the  differences 
in  v  for  successive  values  of  M.  When  the  first  proof  was  received  from  the 
printer,  it  was  subjected  to  three  revisions;  (i)  it  was  compared  with  the  original 
manuscript,  one  of  us  reading  the  manuscript  while  the  other  followed  the  proof. 
(2)  The  differences  in  v  for  successive  values  of  M  (but  for  the  same  values  of  e} 
were  constructed  from  the  printed  tables  and  compared  with  the  differences  that 
had  already  been  set  into  type.  (3)  The  differences  in  v  for  successive  values  of 
e  (but  for  the  same  values  of  M)  were  constructed  from  the  printed  table  and 
were  seen  to  run  smoothly.  The  care  with  which  the  tables  had  been  computed, 
copied  and  set  into  type  may  be  inferred  from  the  fact  that  two  and  one  half 
errors  were,  on  the  average,  found  on  each  page  of  the  proof.  The  second  and 
third  revisions  together  revealed  about  twenty-five  errors. 

Although  the  computations  were  carried  out  to  three  decimal  places,  and  then 
rounded  off  to  the  nearest  hundredth,  the  error  in  the  printed  numbers  will  occa- 
sionally exceed  o°.oo5.  In  all  doubtful  cases  the  computations  were  repeated 
with  seven-place  logarithms.  But  in  order  to  make  certain  in  some  cases,  it  would 
have  been  necessary  to  start  with  values  of  E  that  extend  beyond  the  third  decimal 
place. 


TABLES    FOR    THE    TRUE    ANOMALY.  3 

To  obtain  v  corresponding  to  a  value  of  M  greater  than  180°,  the  latter  should 
be  entered  with  the  argument  360°    -  M  and  the  resulting  value  of  v  counted  as 
negative.     Thus  for  ^  =  0.07  and  M  =  250°,  we  find  opposite  no0  that  v  =  - 
ii7°.3o,  and  this  is  equal  to  242°. 70. 

Simple  or  linear  interpolation  for  the  fractional  part  of  M  is  almost  always 
sufficient;  thus,  if  e  does  not  exceed  0.50  the  neglect  of  second  differences  cannot 
cause  an  error  of  more  than  o°.oi.  With  higher  values  of  e  this  error  becomes 
appreciable  for  a  small  portion  of  the  tables  near  the  beginning.  Thus  for 
e  =  0.77  and  M  near  4°  this  error  may  reach  o°.i3.  The  computer  may  take  this 
into  account  by  always  adding  a  correction  to  the  numerical  value  of  v  that  has 
been  obtained  by  simple  interpolation.  This  correction  is  obtained  by  multiply- 
ing the  second  difference  (the  difference  between  two  successive  tabular  differ- 
ences) by  the  number  in  the  following  table.  The  argument,  (x\,  is  the  frac- 
tional part  of  M,  and  may  have  any  value  from  zero  to  unity. 

x.  Factor  for  the  Second  Diff< 

0.0       0.00 

O.I     0.04 

0.2      OX>8 

0.3     0.10 

04    o.u 

0.5    o.xz 

0.6     o.iz 

0.7     o.io 

0.8     ox>8 

0.9  0x14 

I.O    .  .    O.OO 


TABLES    FOR    THE    TRUE    ANOMALY. 


M 


e  =  .01 


.02 


.03 


e  =  .04 


.05 


.06 


e  =  .07 


0 

1 

2 
3 

4 

5 
6 
7 
8 
9 

10 
11 
12 
13 
14 

15 
16 
17 
18 
19 

20 
21 
22 
23 
24 

25 
26 
27 
28 
29 

30 
31 
32 
33 
34 

35 
36 
37 
38 
39 

40 
41 
42 
43 
44 

45 
46 
47 
48 
49 

50 
51 
52 
53 
54 

55 
56 
57 
58 
59 

60 


o.oo 

1.02 

2.04 


9.18 

IO.2O 
11.22 
12.24 
13.26 
14.28 


20.4O 
21.41 
22.43 
23-45 
24-47 

25-49 

27-53 
28.54 


31.60 
32.61 
33-63 
34-65 

35-66 
36.68 
37-70 
38-71 
39-73 
40.74 

42-77 
43-79 
44.80 


49.87 
50.88 


53-92 
54-93 

55-94 


57-97 
58-98 
59-99 
61.00 


.02 

.02 


'° 

• 


O.OO 

1.04 
2.08 

3-12 
4.16 

5.20 
6.25 
7.29 

8-33 

9-37 

10.41 

u-45 
12.49 


15.61 


18.72 
19.76 

20.80 
21.84 

22.88 

23.92 
24-95 

25.99 
27.03 
28.06 


1.04 
1.04 

1.04 
1.04 

i. os 

1.04 

1.04 
1.04 

1.04 

1.04 
1.04 
1.04 

1.04 
1.03 
1.04 
1.04 


1.04 


1.04 
1.03 


36.34 
37-37 
38.41 

39-44 
40.47 


1.03 


1.03 


1.03 

1.03 


49-73 

51.78 
52-81 
53-83 
54-86 
55-88 


59-97 
60.99 

62.01 


s 


, 

1.02 


O.OO 

1. 06 

2.12 


10.62 
11.68 


I9.IO 
2O.I6 

21.22 

22.28 
23-33 


28.61 
29.67 

31.78 
32.83 

33-88 
34-93 
35-98 

37-03 
38.08 

39-13 
40.18 

42-27 
43-32 
44-36 


s 


i. 06 
1.06 

1.06 

"S 


.06 


47-50 
48.54 
49.58 
50.62 

52.70 

53-73 
54-77 
55-81 

57-88 
58.91 
59-94 
60.97 
62.00 

63-03 


.05 
.05 
.05 
•OS 

.os 
.05 

•  OS 


- 


n-i 


0.00 

1. 08 
2.17 
3-25 

4-34 


i. 08 


,.08 


8.67 

9-7? 


SS 


i. 08 
i. 08 
i. 08 

1.09 
1. 08 


1949 

21.64 

23.80 
24.88 

27.03 
28.10 
29.18 
30.25 

32.40 

33-47 
34-54 
35-6i 
36-67 


,„ 
T  „. 

I06 
I'°6 
1.07 


37-74  .  OT 

ss 


42.00 


49.41 
50.47 
51-52 
52.57 

53.63 
54-68 
55-72 
56.77 
57-82 


60.95 


i. 06 

05 OS 

i. os 

1. 06 

i. os 


1.04 


'-04 


O.OO 
I. II 
2.21 


5-53 
6.64 

7-74 
8.85 

9-95 

11.06 
12. 16 


15-47 
16.58 

18.78 

20.98 

22.08 
23.18 
24.28 
25.37 
26-47 


A 
i. ii 


I'xo 
1.  1  1 


'-10 

1.  10 


i. 09 

I.IO 

1.09 


28!66  '•' 


3'-94  — 

m 

37-38  ;;°g 

38.46  ' 


4279  I'°8 

'  1.07 

43-86 

44-94  -°g 
46.02 

47-°9  I'll 

48.16  |'°7 

49-23  . 

5°-3°  ,:„ 


54-57 
55-63 
56-69 

57-75 
58-81 

59-86 
60.92 


A 

1. 13 
1. 13 


T 
"-13 


x'13 


1.  13 


O.OO 

1-13 

2.26 
3-39 

5-65 
6.78 
7-90 
9-03 
10.16 

11.29 

12.42 

13-54 
14.67 

15-79 
16.92 
18.04 
19.17 
20.29 
21.41 

22.53 
23-65 
24-77 
25-89 
27.00 

28.12 
29.23 
30.34 
31-45 

33-67 
34-78 
35-89 
36.99 
38.10 

39-20 
40.30 


43-59  I'] 


1. 12 
1. 12 

11 II 

1. 12 

I. II 
I. II 
I. II 


.  „ 

' 

!'" 

;•; 

'•" 

1.  10 


64.07 


64.07 
65.12 


i.  05 


49-04 
50.13 


53-37 
54-45 

55-52 
56.60 
57-67 
58-74 
59-81 

60.87 
61.94 
63.00 
64.06 

66.17 


1.09 


r-°8 

'-07 
1-07 


O.OO 

1-15 

2.31 

3.46 

4.61 

5-77 
6.92 
8.07 
9.22 
10.38 


13.82 
4-97 


i. if> 

I. IS 


18.41 
19-56 
20.70 
21.85 

22.99 
24-13 

26.41 

28.68 
29.81 

30.95 
32-08 

33-21 

34-33 
35-46 
36.59 
37-71 
38-83 

39-95 
41.07 
42.18 
43-30 


1.14 

I. IS 

1. 14 

15 IS 

1.14 
1.14 

1. 14 


1. 13 


,  „ 
'  3 

'  3 


45-52 
46.62 

47-73 
48.83 
49-93 

51-03 
52-13 
53-23 
54-32 
55-41 


59-75 
60.82 

61.90 

62.97 
64.04 
65.11 
66.18 

67.24 


! 


r-07 
1-07 


I'07 
i.  06 


2 
3 
4 

5 
6 
7 
8 
9 

10 
11 
12 
13 
14 

15 

16 
17 
18 
19 

20 
21 
22 
23 
24 

25 
26 
27 
28 
29 

30 
31 
32 
33 
34 

35 
36 
37 
38 
39 

40 
41 
42 
43 
44 

45 
46 
47 
48 
49 

50 
51 

52 
53 

54 

55 
56 
57 
58 
59 

60 


0 


TABLES    FOR    THE    TRUE    ANOMALY. 


If 


.01 


e  =  .02 


.03 


e  =  .04 


e  =  .05 


.06 


.07 


M 


60 
61 
62 
63 
64 

65 
66 
67 
68 
69 

70 
71 
72 
73 
74 

75 

76 
77 
78 
79 

80 
81 
82 
83 
84 

85 
86 
87 
88 
89 

90 
91 
92 
93 
94 

95 
96 
97 
98 
99 

100 
101 
102 
103 
104 

105 
106 
107 
108 
109 

110 
111 
112 
113 
114 

115 
116 
117 
118 
119 

120 


61.00 
62.01 
63.02 
64.03 


66.04 
67-05 
68.06 
69.07 
70.08 

71.08 


73-09 
74.10 

76.11 
77-12 
78.12 
79.12 
80.13 

81.13 
82.13 


86.14 
87.14 


SS 

93'15 

94-  '4 

95-14 


3:3 

J 


102.12 


.01 
.01 


01 

M 
oo 

0, 

oo  I 


.00 

.00 
.00 

Jft 


099 


106.10 

107.10  1-°° 
108.09  °'99 I 
109.08  °-99  i 

110.08  I-00' 


0.99 


111.07 
112.06 
113-06 

114.05 


116.03 
117.02 
118.01 
119.01 
I2O.OO 

120.99 


°'99 
°'99 
'-00 

°'" 
0.99 


62.01 

63.03 
64.05 
65.06 
66.08 

67.10 
68.12 


71.16 

72.17 
73-18 
74-20 
75-21 


77-23 
78.24 

79-25 
80.25 
81.26 

82.27 

83-27 
84.28 
85-28 
86.29 

88.29 


S3 

'4:3 


—5     o 


104.23 

105.22 

106.21 


.02 
.02 
.01 
.02 

.02 

.02 


o.oo 

°-99 

°'99 
0.99 


°'99 


IO7.2O 
108.19 
109.18 

116.16  °'98 

1  11.15  " 


0.99 
117.06 
118.04   °'98 
119-02   °'98 
I20.OO  °     g 

120.98   °'9. 
0.98  , 

121.96 


64.06 
65.09 

66.il 

68.16 
69.19 
70.21 


73-27 
74-29 
75-30 
76.32 

78.35 
79.36 


82.40 

8441 
86!42 

88.43 

89-44 
90.44 
91.44 


93-44 
94-43  £ 


97.42 


0.09 


0.99 

101.38    °-99 

IO2.37      ' 

"    0.99 

103-36   „ 


0.09 
IO8.29 
109-27    °-9° 
110.25      ' 


"5:1! 


118.06 
1  19-04 
120.0! 


-» 


°'98 
°-97 


65.10 
66.14 
67.18 

68.21 

69-24 
70.27 

7I-30 
72-33 
73-35 

74-38 
75-40 
76.42 
77-44 


80.50 
81.51 
82.52 

84-55 
85-56 


87-57 
88.58 

89.58 


93-58 


04 


.03 


.03 


>     O  < 

97-56 
98-55  °;; 

99-54  0.00 

IOO-53  o  99  ' 
101.52 

102.50  °' 

I03-49  °;^ 

104-47  „ 


!3£3 


118.10  °'97 
0.97 


122.92 


122  QI    "•'* 

'9     0.96 
123.87 


66.16 
67.20 
68.25 


70-33 

72.40 

73-43 
74.46 

75-49 
76-52 
77-55 
78.57 
79-59 
80.62 
81.64 
82.65 
83.67 
84.68 

85.70 


87.71 
88.72 

90-73 


93-73 
94-72 


.03 


97.70 
98.69 
99-68 

100.67 
101.65 
102.63 
103.61 
104-59 
105-57 


109.47 

' 


°'" 


0.99 
0.98 


0.97 


"3-34 


117.18 


120.05 


0.95 

121.01  °-<* 
121-96  °'9* 
122-91 


I24.8I 


68.28 
69-33 


72-47 
73-51 

74-54 
75.58 

76.62 

77-65 
78.68 

79-71 


81.76 
82.78 
83.80 
84.81 

86.84 
87.85 
88.86 
89.87 
90.88 

91.88 
92.88 
93-88 
94.87 
95-87 


04 


106.67 
107.64 

108.61 


110.54  o'9^ 

m 

"5-33  °;^ 

116.29 

I  IT   ->,     °-°S 


Ii9:i4°-95i 
120.08  °'94  ' 

0.95 


°-94 


122.91 

iss  - 

V   0.94 
125-73 


69.36 
70.42 


73-58 

74-62 
75-67 
76.71 

77-75 
78.78 
79.81 
80.85 
81.88 

82.90 
83.92 
84-95 
85-97 
86.98 

88.00 
89.01 
90.02 
91.02 
92.02 

93-03 
94-02 
95-02 
96.01 

97-99 

98.98 

99.96 

100.95 

101.93 


05 


•79  « 


1 11.60  "' 

0.95 

114.46  °"9S 
IIS  41    °'9S 

"6^35  °'94 

00  0.95 
117.30 
118.24  °-94 
II9I8  °'94 
120.12  °'94 


124.79 
125-71 
126.64 


0.93 


60 
61 
62 
63 
64 

65 
66 
67 
68 
69 

70 
71 
72 
73 
74 

75 
76 
77 
78 
79 

80 
81 
82 
83 
84 

85 
86 
87 
88 
89 

90 
91 
92 
93 
94 

95 
96 
97 
98 
99 

100 
101 
102 
103 
104 

105 
106 
107 
108 
109 

110 
111 
112 
113 
114 

115 
116 
117 
118 
119 

120 


TABLES  FOR  THE  TRUE  ANOMALY. 


M 


.01 


e  =  .02 


.03 


e  =  .04 


.05 


.06 


.07 


M 


120 
121 
122 
123 
124 

125 
126 
127 
128 
129 

130 
131 
132 
133 
134 

135 
136 
137 
138 
139 

140 
141 
142 
143 
144 

145 
146 
147 
148 
149 

150 
151 
152 
153 
154 

155 
156 
157 
158 
159 

160 
161 
162 
163 
164 

165 
166 
167 
168 
169 

170 
171 
172 
173 
174 

175 
176 
177 
178 
179 

180 


j;^!  °-" 
i22-97  ::ii 

I23'95  0  99 
124.94 

0.99 


126.92 

!3S 


0.99 


'33-83 
'34-82 


•0"-/V    „  9g 

138:76  °'99 

I«)  75    °'99 

'39.75  0-98 

'4°-73  o  98 
141.71 

isi 
If = 

149-58  °'9 


'5°-57 


0.08 

°-98 


'54-50 


157-44 
158.43 
159-41 
160.39 


°-98 


168.24 
169.22 

170.20 


°-98 
0.98 


0.98 

'77^  °;98 
179.02 


180.00 


8 


121.96 


126.85 
127.83  °-98 
128.80  °-9' 
129.78  °-98 
'30-75  - 


133-67 
134-65 
135-62 


146.48 


°-97 
0.97 


143-38  "• 
144-35  *„ 
145-32  HI 

146.29 
147.26  °-9' 

148.22  °'96 
'49-19  °'9I 
150.15 


151.12 


0.97 
0.97 


154.02 

'54-98 


157-88 
158.84 
159.80 

160.77 


0.97 


0.96 
0.96 

0.96 


179-04  0\l 
180.00 


122.92 


285 


S 


« 

0.96 


ss 


140.24 


143.10 
144.05 
145.01 
I45.96 
146.91 


0.95 

151.67  0  94 

«53§  "95 

154-51  ° 

15546    ' 


0 


157-35 
158.30 


7  0.95 
161.14 
162.08  °'94 
163.02  Ol 

163-97  °' 
164.91  Q   4 

165.86 
166.80  °'94 

167.75  °' 
168.69  °' 

1 69-63  °'9! 


172.46 

'73-40 
'74-35 


177.17 

179.06 
180.00 


°-94 
°-9s 

0.94 


128.65 

-9-60  ::ii 

0.95 


'SS  HI 

US  °- 

'37-'8 :- 


140.01 
140.96  °'9S 

O.QA 

'4'-9°  0.94 
142.84 


149-39 
150.33 

152.20 


0.01 


154-99  „  .: 
I55-92  0 

156.85 
157.78  * 
158.71      93 

159-64  °'93 
160.57  °'93 

'  0.93 
161.50 
162.42  °'92 

I63-35 
164.28 

165.21  °'93 
0.92 

166.13 
167.06  °'93 
167.98  °'92 
168.91  °'93 
'69.83  °-9* 


I72.6I 

173-53 
174.46 

175.38 


°'93 


179.08 
iSo.OO 


I24?8l  A 

125-75  °'94 

126.70  °'9S 

127.64  °'94 

128.59  °'9S 

y  0.94 

I29-53  0.94 
130.47  0 

l£g  o 

'33-2  0.93 
134.21 

136.08  °"93 
137.02  °'94 
137.95  °'93 

J/-y;>  0.93 
138.88 

139-81  °'93 

I4O.73  "9 

141.66  °'93 

142.59  °;93 

143-51 
144-43 
145-36 
146.28 
147.20 


°-92 
0.92 


°'93 


148.12 
149-05 
149-97 " 
150.88  °-91 
151.80  °-92 

0.92 

152.72 

(.   0.91 

T  e   ee  O.92 

i«ig  °-91 

0.92 
O.9I 


159.12 
160.03 


I6I.85 
162.76 
163.67  ° 
164.58  °'91 
165.49  Q- 

I66.4O 

167.31  °'91 
168.21  ° 
169.12  °'91 

170.03  °'91 
0  0.91 

I7O.94 

171-84  °-9° 
172.75  . 
173.66  "•• 

174.56  ' 
0.91 


177-28 
178.19 
179.09 

180.00 


127.60 


132.25 
134.10 

136.86 
139.61 


0.93 
093 


0.92 

0.92 
0.92 


142.35 
143.26 

144.18 
145.08 

145-99 
146.90 


0.92 


0.90 


iss 


162.20 
163.09  °'89 
'63.98  °'89 
164.87  °'89 

'65-77  n9 
166.66 

,£.-  ,,  0.89 


O.89 
0.89 

0.89 


175.56 
176.45 

179.11 
ISO.OO 


8Q 

9 


'30-33 


'33-07 
'33-99 
'34-90 


'38-53 
'39-43 


0.0 


142.13 
I43.03 

I44.83 


O.90 
0.89 


147.51 
148.40 

149.29 


- 


-    o. 


153-73 
154.61 

155-49 
156.38 
157.26 

158.14 
159-02 
159.90  l^l 
l6O.78    ' 

161.66  °'88 
0.87 

162.53  n  8R 

l63-4'  o  M 
164.29  °'88 

165.16  °' 
166.04 

166.91 
167.79 
168.66 
169.54 


.88 


171.28 
172.16 
I73.03 
I73.90 
174-77 

175.64 
176.52 

177-39 

179.13 
180.00 


120 
121 
122 
123 
124 

125 
126 
127 
128 
129 

130 
131 
132 
133 
134 

135 
136 

137 
138 
139 

140 
141 
142 
143 
144 

145 
146 
147 
148 
149 

150 
151 
152 
153 
154 

155 
156 
157 
158 
159 

160 
161 
162 
163 
164 

165 
166 
167 
168 
169 

170 
171 
172 
173 
174 

175 
176 
177 
178 
179 

180 


TABLES    FOR    THE    TRUE    ANOMALY. 


M 


e  =  .08 


e  =  .09 


.10 


e  =  .11 


.12 


.13 


.14 


M 


0 

1 

2 
3 

4 

5 
6 
7 
8 
9 

10 
11 
12 
13 
14 

15 
16 
17 
18 
19 

20 
21 
22 
23 
24 

25 
26 
27 
28 
29 

30 
31 
32 
33 
34 

35 
36 
37 
38 
39 

40 
41 
42 
43 
44 

45 
46 

47 
48 
49 

50 
51 
52 
53 
54 

55 

56 
57 
58 
59 

60 


o.oo 
1.18 
2.36 
3-53 
4.71 

5-89 
7.06 

9-42 
10.59 


14.11 
15-28 

17-63 
18.79 
19.96 

22.29 

23-46 
24.62 
25-78 
26.94 

29.26 
30.41 

32.71 
33-86 

35-01 
36-16 
37-30 
38.44 
39-58 

40.72 
41.85 
42-98 
44.11 

45-24 

46.37 
47-49 
48.61 

49-73 
50-84 

5I-96 
53-07 
54-17 
55-28 
56.38 

57-48 

59-67 
60.76 


65.10 
66.18 
67-25 

68-33 


18 


18 

17 
18 

a 

17 

>I7 
.18 
.17 
.17 


.16 
.17 

•  17 
.16 

•  17 


O.OO 
1.20 
2.4I 

3-61 


A 

1.20 


9.6l  *'20 

I0'81  \\ll 

12.01 

13-21  '-20 

*•  T    on 


17-99 
19.18 
20.37 
21.56 
22.75 

23-94 
25.12 


66.17 


28.67 

29-84 
31.02 
32.19 
33-36 
34-53 

35-70 
36.87 
38.03 
39-19 
40.34 
41.50 
42-65 
43.80 

44-95 

47-23 
49-51 


1. 19 

1.18 

1. 19 

1.18 
1.18 
1. 17 

1. 17 
1. 17 


i 

;:;* 


1.14 
1.14 


1.14 
1. 13 


52.89 

54-02 

55-14 
56-26 

57-37 
58.48 

59-59 
60.70 
61.80 


I  13 

3 

I    12 


'-09 


o.oo 

1-23 
2.46 

3.69 
4.91 

6.14 
7-37 
8-59 
9.82 
11.04 


15-93 
17-15 


23 
'" 


1.23 


22 


20.80  I-22 

22.01     '•" 


II 


69.42 


37-59 
38-77 
39-95 
4I.I3 

42-30 
43-47 
44.64 
45.80 
46.96 

48.11 

b  <::* 
51.57  i'i* 
52.71 

53.85 

54-99 
56-12 

57-25 
58-38 

59-50 
60.62 

61.74 
62.85 


1.18 
1.18 

I.IS 
1. 17 

1. 17 
1. 17 

1.16 
I.IS 


.  14 


•* 


67.26 

68.35 
69.44 

70.53 


O.OO 

1-25 
2.51 

3-77 

5-02 

6.27 

7-52 

8.78 

10.03 

11.28 

13^8 
15-02 
16.27 

I7-5I 
18.76 
20.00 
21.24 
22.47 
23.71 

24-94 
26.17 

28^63 
29-85 

31-07 
32.29 
33-50 
34-71 
35-92 

37-13 
39-54 


A 
i. 25 


r  je 
5 

I.2S 


*•* 


i.  25 


1.25 


1.23 
i.  33 

1.23 


1.22 
1.22 

1.22 
1. 21 
1. 21 


.  ,. 

'  0 

" 

'  9 


43-H 
44-30 
45-48 
46.66 
47.84 

49.01 
50.18 


1.18 
1.18 
1.18 
1.17 


S6     '    I.is 

54-82 
55-97       * 
57-ii 
58-26    •'* 

59-39  ,;,* 

60.53  . 
61.66       3 

62.78  r 

63-90  '•" 


66.13 
67.24 


71.64 


r 
• 


0.00 

1.28 
2.56 
3.85 


7.69 

8-97 
10.24 

11.52 

12.80 
14.07 

15-34 
16.62 


20.42 
21.68 

22.94 
24.20 

25.46 
26.72 


30.46 

32-94 
34.18 

35-41 
36.64 

39-09 
40.31 
41-53 
42-74 

43-95 
45-15 
46.35 
47-55 
48.74 

49-93 
51.11 
52.29 
53-47 
54-64 

55-8i 


58.13 

59-28 


6i-57 
62.71 

63-85 
64.98 
66.10 

67-23 
68.34 

69-45 
70.56 

72.76 


.28 


.27 
.28 
.28 

.27 

.27 


•  27 

.26 


22 

22 
21 
21 

20 
20 
20 
If 

10 

ll 

18 
It 


•  14 

•  14 
.13 

.12 

.13 

.II 
.II 


O.OO 
2.62 

3-93 


22.14 
23-43 


34-87 
36-13 
37.38 

38-63 
39-87 

42-34 
43-57 

44.80 
46.02 
47-24 
48-45 
49.66 

50.86 


53-25 
54-44 
55-63 

56-81 
57.98 
59-15 


61.48 

62.63 
63.78 

64-93 
66.07 
67.20 

68.33 


• 


6.55  ' 

7-85  '3° 
9.16 

10.47  *'31 

"•77  ;:*: 


,8.27 


1.29 

1.29 


25-99  .  .„ 
27-27  I'll 

28.55  •*! 


•  I4 

'« 


1.22 
1.22 
1. 21 
1. 21 
1.20 

I. 2O 
1. 19 
1. 19 


70-57 
71.69 

73-90 


I.IS 

I.IS 
I.IS 

1.14 

1. 13 
1. 13 

1. 12 
1. 12 
1. 12 


0.00 

i-34 
2.68 
4.02 
5-35 
6.69 

9-36 
10.70 
12.03 

14.69 
16.01 

17-34 
18.66 

19.98 
21.30 
22.62 
23-93 


1.34 


1.33 
1.33 

1.33 


1.32 
•32 


'-30 


26.54 
27-84 

29-'4 ;;-; 
30.44 ' 


34-30 
35-58 
36.86 


50.59 
51.81 

53-02 


1. 25 

I.2S 

1.25 
1.23 

1.22 
1.23 
1.22 

1. 21 
I. 21 
1. 21 


60.19 

61.37 


66.02 

67.17 
68.31 

70.57 
71.70 
72.82 

73-93 
75-04 


o 

'-18 


1.16 
I.IS 

1. 13 

1. 13 

1.13 


0 
1 

2 
3 

4 

5 
6 
7 
8 
9 

10 
11 
12 
13 
14 

15 
16 
17 
18 
19 

20 
21 
22 
23 
24 

25 
26 
27 
28 
29 

30 
31 
32 
33 
34 

35 

36 
37 
38 
39 

40 
41 
42 
43 
44 

45 
46 
47 
48 
49 

50 
51 
52 
53 
54 

55 
56 
57 
58 
59 

60 


8 


TABLES    FOR    THE    TRUE    ANOMALY. 


M 


e  =  .08 


.09 


.10 


.11 


.12 


e  =  .13 


e  =  .14 


60 
61 
62 
63 
64 

65 
66 
67 
68 
69 

70 
71 
72 
73 
74 

75 
76 
77 
78 
79 

80 
81 
82 
83 
84 

85 
86 
87 
88 
89 

90 
91 
92 
93 
94 

95 
96 
97 
98 
99 

100 
101 
102 
103 
104 

105 
106 
107 
108 
109 

110 
111 
112 
113 
114 

115 
116 
117 
118 
119 

120 


A 

i. 06 
1.07 
i. 06 
i. 06 
1.06 

i. 06 


I  u- 1  tj 

76.80 

77.84 

78.88 
79.92 
80.96 
81.99 

84.05 
85.08 

86.10 
87.12 
88.13 

89.15 
90.16 
91.17 
92.17 
93-17 


99-13 
100.11 


1.04 
1.04 


i. 02 

1.02 


103.04 

I04.O2 
104.99 

106.92 
107.88 

108.84 
I09.8O 
110.75 

112.65 
II3.60 
114-54 
115-49 


0.99 
0.99 
0.99 

0.98 

0.97 
0.98 

0.97 
0.96 

O*97 
0.96 

0.96 


0.9S 


°'94 


122.02 

122.95 
123.87 
124.79 
125.71 
126.62 

127-54 


°'93 
0.93 


70.50 
71.57 

72'64 
73-70 


05 
04 

•03 


77-93 
78-98 

80.03 
81.07 
82.11 
83.14 
84.18 

85.21 
86.23 

87-25 
88.27 

89-29 
90.30 
91-31 
92.32 
93-32 
94-32 


97-30  " 
98.29  °'99 
99.28 

100.26 
101.24 

IO2.2I 


.01 
.01 


°'99 
0.98 


°'9 
°'97 


105.12 
106.09  °'97 
107-05 
108.00 


°'96 


°'9S 
°'94 


III.8I 
112.75 
113.6$   °'94 
114.63 

115-57 
116.50 
II744 


0.94 
0.94 
0.93 
0.94 


0.92 


119.29 
120.22 
121.14 
I22.O6 
122-97 

123.89 
124.80 
125.71 
126.62 
127.52 

128.43 


°'93 


0.92 


°-9° 

0.91 


72.69  *-° 

73-76     '° 


75-9°  r  06 

76.96  l*"5 

78.02  '-0* 

79-08  '-06 


83.26 


1.03 
1.03 

86.36 

S7-39  ^ 


90.45 ;;;; 

92'47  |'oo 
93-47      °° 

94-47  . 

95-47  j;oo 
96.47 

97-46  °'99 


«• 


101.39 
102.36  °-97 

"' 


106.22 

107.18  °-96 

108.13  °-9f 

109.09  °-96 

116.03  °-94 

0  0.95 
IIO.98 

111.92  °'94 

112.86  °'94 

113.80  °-94 
114-73 


°'93 
°'92 

°'92 
0.91 


117.52 
119-36 

120.27 
121.19 

122. IO 
123.01 
123.91 

124.82 
125.72 

126.62  °-?° 


129.30 


0.91 


74-89 

75-97 
77.04 


i. 08 
i. 08 
1.07 

I.  O6 

1.06 


• 


84.42 
85.46 
86.49 

87.52 
88.55 
89-57 


92.61 
93.62 
94.62 


1.03 


°-98 

o.oo 


'       0 

°-9 


109.21 
110.16  °'9S 

III. 10  °'94 
0.94 
112.04 
112.97  °'93 
I:3-90  „"* 


116.68 

117.60  °-92 
118.51  °-91 
119.42  °-91 


121.24 
!•>•>  iT 

122.  14 


78.19 

80^32 
81.38 

83-49 

85^58 
86.62 
87.66 

88.69 
89.71 
90.73 
91-75 
92.76 


r 

I.OO 

S 


1.04 

1.03 

1.02 
1.02 
1.02 
I  .OI 
I.OI 


95-77  I00 
96.77 

97-76  °'99 

0.99 

99  71  °'98 

lOC^I  °'98 

101.68  °"97 

102.65  °'97 

0  0.97 
IO3.62 

-4.58  °;96 

Io6-50  °'9t 


I08'4°  0.94 

109.34 

110.28  °'94 

1 1 1.22  °'94 

112.15  °'93 

0  0.93 
II3.O8 

0.93 


117.68 
118-59    ° 
119.50   ~" 
I2O.4O 
121.30   °-9° 

122.19 

0.00 

!li  a 


130.16 


I26'64 


131.01 


0.88 


73-9° 
75.00 

76.09 
77-18 


81.48 

82.55 


84.66 
85-70 
86.75 
87-79 
88.82 

89.85 
90.87 
91.89 
92.91 
93-92 
94.92 
95-92 
96.92 

97-91 


•  03 


°-99 

°0;99 


101.84 

102.80 

-3-77 


106.64  °-9 


°'92 


l^.2S  °'93 

113.20  °-92 

0.92 
114.12 

115.04 

115.96  "•"• 

116.86  °-90 

"7-77  °;9| 
118.68 


0.90 
0.89 
0.89 

0.88 
0.88 


126.66 

127-53 
128.40 
129.27 


131-85 


a 


A 

7p4  ;:£ 
80.50 

£S  a 


1.04 

1.03 
1.03 


86.88 
87.92 
88.96 
89.99 

91.02 

92.04  *' 
93-06  ' 

94-07   . 
95-oS  i'Qo 

96.08 
97.07  °'99 
98.07 
99.06  °-99 

IOO-°4  o^s 

IOI.O2 
101.99  °  9' 
102.96  °'97 
1 03-92  °'9, 


107.74  °-9S 

108.68  °'94 

109.62  °'94 
0.93 


°-93 


112.40 


0.91 


116.97 
117.87 

119.66 


a 


124.08 

I24-95 
125.82 
126.69 


0.88 
).87 


'  7 


132.67 


60 
61 
62 
63 
64 

65 
66 
67 
68 
69 

70 
71 
72 
73 
74 

75 
76 
77 
78 
79 

80 
81 
82 
83 
84 

85 
86 
87 
88 
89 

90 
91 
92 
93 
94 

95 
96 
97 
98 
99 

100 
101 
102 
103 
104 

105 
106 
107 
108 
109 

110 
111 
112 
113 
114 

115 
116 
117 
118 
119 

120 


TABLES    FOR    THE    TRUE    ANOMALY. 


M 


e  =  .08 


e  =  .09 


.10 


e  =  .11 


e  =  .12 


e  =  .13 


.14 


Jtf 


120 
121 
122 
123 
124 

125 
126 
127 
128 
129 

130 
131 
132 
133 
134 

135 
136 
137 
138 
139 

140 
141 
142 
143 
144 

145 
146 
147 
148 
149 

150 
151 
152 
153 
154 

155 
156 
157 
158 
159 

160 
161 
162 
163 
164 

165 
166 
167 
168 
169 

170 
171 
172 
173 
174 

175 
176 
177 
178 
179 

180 


130.27 
I3i.  i8 

132.08 


136-58 
137.48 
138.37 


0.90 

0.91 
0.90 
0.90 


0.89 


145.47 

146.35 
147-22 


0.87 

0.88 
0.87 

0.88 
0.87 


'53-34  °;8; 

ig:08  °-87 

155-95  °0H 
156.82  °'87 
157.68 

158.55 
15942 
160.28 
161.14 
162.00 

162.86 
163-73 
'64-59  u'°" 
165-45  ° 
166.30  ^ll 

167.16 
'68.02  °-8* 
168.88  °'8, 


86 


-    g, 

° 


0.86 
0.87 


174.87 

175-73 
176.58 

177-44 
178.29 


"•" 


129.33 
130.22 


°'89 


'35-58  I'8 
^46 


142.61 
143-48 
144-35 
145.22 

146.09 
146.96 
147.82 
148.69 
149-55 


0.87 
0.87 
0.87 
0.87 

0.87 
0.87 


„  Rfi 

°-8< 

»•!* 


I53.84 

I54-69 
155-55 
156.40 
I57.25 
158.10  uo-tl 

158.95   0 
'59-80  °OBS 
160.65  °1* 
161.49 
162.34 


163.19 
164.03 
164.88 
165.72 
166.56 

167.41 
168.25 
169.09 


0.85 


180.00 


174-97 
175.81 
176.65 

1/7-49 
178.32 
179.16 

180.00 


a 


' 


129.30 


g 


134.6 

137.23 
138.10 


0.88 

* 


087 


'45-85 


:•- 


158.51 
159-34 
161.01 

163.50 

165.16 

165-99 
166.82 

167.64 


«•• 


. 

; 


g, 

: 


'75-07 


138.84 

'39-69 
'4°'54 
141.40 


143.09 
'43-94 
144.79 

I45.63 
146.47 

H7.3I 
148.15 


'54-80 


'59-73 


163.81 
164.63 


167.88 
168.69 


0  82 


* 

• 


'73-54 


180.00 


179.19 
180.00 


0.81 
0.8I 


131.01      . 
131.88  °'87 

•32-74  °;86 

133-60     ™ 
'34-46  3 


lyjtn  °-8s 
'38-72  °0\ll 

139-56 
140.41  °-8* 

142.08  °'83 

'43-75  „ 
144-59  „ 
I45-42  ° 
146.25 

I47.07  ° 


147.90 


152.01 


156.07 

156.88 


i6o.n 


g 


°-8 


162.52 


0.80 

165.71  °"79 
166.51  °'8° 

l68.il 
168.90  °'79 
169.70  Ol 
170.49     ' 

0.79 
172.08 
172.87  °'79 
'73-67  °'8° 


180.00 


- 

0.79 


136.09 
136.93 
137-77 
138.61 

139-44 


141-93 
142.76 


H6:04  °-8* 
146.86  °'82 

147.67  ° 

'  0.81 

148-48   . 


III; 


160.48 
161.27  °'" 
162.05  °'78 
162.84  °'79 


164.41 
165.20 


168.33  0 
169.11  °' 
169.89  °'78 
170.67 
'''•45 


0.78 
0.78 
0.78 


174  56  °'77 
175-34  I'.H 
176.12 
176.89  °'77 
177.66  °'77 

'o  .,  0.78 

178-44  „  ,„ 

179.22  °'78 

0.78 

180.00 


ss 


136.02 

136-85 
137-68 
138-51 
139-34 


3 


0.8I 


145.04 


149-05 
149.85 

*- 

150-64 


'56-95 
'57-73 
'58-5' 
'59-28 


0.79 

0.78 
0.78 


164-70 

I65'47  I'll 
166.24 
167.01  °'77 


°-76 


176.08 


175-43 
176.19 


178.48 
179.24 

180.00 


120 
121 
122 
123 
124 

125 
126 
127 
128 
129 

130 
131 
132 
133 
134 

135 
136 
137 
138 
139 

140 
141 
142 
143 
144 

145 
146 
147 
148 
149 

150 
151 
152 
153 
154 

155 
156 
157 
158 
159 

160 
161 
162 
163 
164 

165 
166 
167 
168 
169 

170 
171 
172 
173 
174 

175 
176 
177 
178 
179 

180 


10 


TABLES    FOR    THE    TRUE    ANOMALY. 


M 


.15 


e  =  .16 


.17 


.18 


.19 


.20 


.21 


M 


0 

1 

2 
3 

4 

5 
6 
7 
8 
9 

10 
11 
12 
13 
14 

15 
16 
17 
18 
19 

20 
21 
22 
23 
24 

25 
26 
27 
28 
29 

30 
31 
32 
33 
34 

35 
36 
37 
38 
39 

40 
41 
42 
43 
44 

45 
46 
47 
48 
49 

50 
51 
52 
53 
54 

55 
56 
57 
58 
59 

60 


o.oo 
1-37 
2-74 
4.10 

5-47 
6.84 
8.20 

9-57 
10.93 

13-65 
15-01 
16.36 


r-37 


1.36 


I9'°7  1-34 
20.41 

21.76  X'3S 

23-10  J'34 


••" 


i  31 

:•  : 

'-30 


27.IO 
28.43 
29.76 
31.08 

33-70 


• 


£8 


50.31 
51-55 

52.78 
54.01 

55-23 
56.45 

57-66 

58.86 
60.06 
61.25 
62.44 
63.62 

64.79 
65.96 
67.12 
68.28 
69-43 


„ 
3 


1.20 
1. 19 


I.I7 


I.I4 
I.I4 


72.84 

73-97 
75-09 

76.20 


o.oo 
1.40 
2.80 

5-59 
6.99 

8-39 

9.78 

11.17 

13-95 
15-34 
16.72 
18.10 
19.48 

20.86 
22.23 
23.60 
24.96 


,„ 
'to 


.39 


8 


29.03 


33 


.36 
.36 
1.36 

1.35 
1.35 

33-07    l\H 

34-40 
35-73    . 
37-06    '•" 
38.38    I'3' 
59-69    I3I 
41.00 
42.30      ' 
43.6O       •* 

&  I- 


5-  • 


55-01 


57-47 
58-69 

59-91 
61.12 
62.32 


! 


.  Ig 
• 


65.89 
67.07 
68.24  II17 

69.40    •? 

70-56  l?s 


73-99 
75-12 
76.24 


o.oo 

1-43 
2.86 
4.29 

5-72 


IO.OO 

11.42 

12.84 

14.26 


1.43 
1.42 

1.43 


1.42 


22 

24-" 

25.50  '• 


74.01 

75.15 
76.28 

77.41 
78.53 


Mi 


28-27 


35-12 
36-47 
37-82 

40.50 

41.83 
43-15 
44-47 
45-78 
47.08 


50.95 
52.23 
53-50 

54-77 
56.02 

57-27 

59-75 
60.98 
62.20 
63.41 
64.62 
65-82 

67.01 
69.37 


1.38 
1.38 
1.37 
1.36 
1.36 

1.35 


3 

'-30 
1.30 


.  2! 
' 


i. 20 

1. 19 

1.18 
1.18 
1. 17 


1.13 
1.13 
1. 12 


0.00 

2.93 

4-39 

5-85 

7-31 
8-77 


14.58 

i6-°3 

17-47 


21.78 
23.21 
24.64 
26.06 

28.88 


33-08 
34-47 
35-86 

37-23 
38.60 

39.96 


44.02 

45-35 
46.68 
48.00 

49-32 


53-22 
54-51 

55-79 
57-o6 

59-57 


62.06 
63.29 
64.51 

65-73 
66.94 

68.14 
69-33 
70.51 
71.69 

74.02 
75-17 
76.32 
77.46 
78.59 

79-71 


A 
.46 

•  47 


• 


s 


; 

• 


o.oo 


A 
1.50 


4-49 
5-98 

7.48 
8.97 


1.50 


I4-9I 


1.47 
1.48 

1.47 
22.27 

Si8  [H 
26.63 

28.07  ''44 
'    1-44 

5o;94 ;;« 

55-7?  \4' 
35-20  j"Jj 

36.61  . 

38.01  x 

39-40  !' 

40.79  T' 


45-54 
44-90 

¥,?, 


50.28 

51.60  3 

52-92  I'3' 

54-23  T  ,„ 

55-; 
56.82 


1.29 


63.16 

64.40 

65.63 

66.86 


72.85 

74-03 


79-77 
80.90 


o.oo 

1-53 
3.06 

4-59 


A 
1.53 


. 
9'17      5 

' 


13.73  l\ll 

15.25  . 
16.76  •» 

To  «-  1.51 


22.76 
24.25 

f 

g£ 

28-68 


33.06 
34-51 

35-95 

37-38 
38.81 
40.22 
41.63 
43-03 


J.iO 


1.44 

1-43 
1.43 

1.41 


47-18 


49-91    z 

51.26 
52.60   ' 

53-93  . 
55-26 

56-57  , 

57-88 
59.18 


:-s 


ts ::" 

69.22 '•" 

*  1.22 


72.84 
74.03 

76.38 

78.69 

79.83 
80.97 

82.10 


I. IS 

1.14 
1.14 

1. 13 


o.oo 
1-56 
3-i3 


I.S7 
1. 57 


10.94 
12.50 
I4.05 


18.68 

20.22 


53! 


X'S* 


33-78 
36.72 

38.17 
39.62 
4I.O6 

45-33 


^ 
I>47 
1.45 


49-51 


.  ,„ 
-3» 


52.26 

55-62  x-3° 

54.96  x'34 

56.30  '34 

57-63 ,;" 
58.95 ,' 

60.26  I-3X 

61.56  r-3° 

62.85  ;•'' 


- 


67.91 

69-15 
70.38 

71.60 
72.82 
74.02 
75-21 
76.40 

77-57 
78-73 

81.03 
82.17 

83-30 


1.17 
1.16 


0 

1 

2 
3 

4 

5 
6 

7 
8 
9 

10 
11 
12 
13 
14 

15 
16 
17 
18 
19 

20 
21 
22 
23 
24 

25 
26 
27 
28 
29 

30 
31 
32 
33 
34 

35 
36 
37 
38 
39 

40 
41 
42 
43 
44 

45 
46 
47 
48 
49 

50 
51 
52 
53 
54 

55 
56 
57 
58 
59 

60 


TABLES    FOR    THE    TRUE    ANOMALY. 


II 


M 


.15 


e  =  .16 


e  =  .17 


e  =  .18 


e  =  .19 


.20 


e  =  .21 


M 


60 
61 
62 
63 
64 

65 
66 
67 
68 
69 

70 
71 
72 
73 
74 

75 
76 
77 
78 
79 

80 
81 
82 
83 
84 

85 
86 
87 
88 
89 

90 
91 
92 
93 
94 

95 
96 
97 
98 
99 

100 
101 
102 
103 
104 

105 
106 
107 
108 
109 

110 
111 
112 
113 
114 

115 
116 
117 
118 
119 


77-31 
79-50 


81.67 

83*82 
84.89 
85-95 
87.00 
88.05 
89.09 

90.13 
91.16 

92.19 


as 


i. 08 

1.07 


-       ,  o 

98-23 


0.97 


105.04 
105.99 
106.94 
107.88 
108.82 


°'94 


II2'53 

"3-45 


ft- 


"9-75  •£ 
I*?'*4  »••• 

0.88 


I22'4° 


0.87 


I26'73 


s  a 

130.97   0 
'3'-8'   oil 


120     I  133.48 


77.36 

79-57 
80.67 


83-93 
85.00 


88.18 

90-27 
9I-30 

93-35 
94-37 
95.38 


97-39 

98-38 
99-37 


.11 
.10 


I01'33 
I02'3° 


M 
05 


00 
0.99 


o  97 
0.97 


106.14  °-95 
107.09  °-95 

'  0.94 


109.90 
116.83  °'93 

111.75 
'* 


112.67 
"3-58 

114.49 


9 
0.92 


"8-97 
"9-85 


!  123-34 


s 
°0.?7 


I25'92 


a 
a 


130.14 


78.53 

8075 
81.85 


85-11 
86.18 

87-25 
88.31 

89.36 
90.40 
91.44 
92-47 
93-50 

94-52 


.04 
.04 
.03 


99-53 

I00-si 

I01'49 
I02'47 


O.99 

0.98 
0.98 


I04'39 


°'94 


106.30 
107.24 

108.18 

0.94 
IO9.I2 
IIO.O5  °' 
IIO-97  ° 
111.89  °' 

II2.8I    °'9 
O.9I 


"7-30 


79-71 
80.83 
81.94 


85-22 
86.30 

8S!43 
89-49 

90.54 

92.62 

93-65 
94.67 

95.69 
96.70 

97-70 
98.70 
99.69 

100.68 
101.66 
102.63 


107.40 


ogg 
01 


:s 


134.28 


126.82 

127.66  °-*4 

"8-50  °-* 


!£:!?  °-82 
f  0.82 

0.82 

0.8 1 
1  •*•*••"*  0.81 
I35-07 


:ss 


126.88 


131-82 

133-44 
134-25 
I35-05 

135.85 


.08 


.02 
.02 

.00 

.00 
0.09 

0.97 


« 

0.93 


I  IO.2O 
III.I2 
112.04 


"7-43 


120.06 
120.92 


0.85 
0.85 
0.84 

0.83 

0.83 
0.83 
0.82 
0.82 
0.81 

0.81 


0.80 


82.02    ' 


86.41 
87.49 
88.56 
89.62 
90.68 

91.72 

93-80 
94.82 
95-84 
96.86 
97-86 
98.86 


0.98 
101.82 
102.79  °'97 

104.72  0-96 
105.67  °'9S 

'  0.95 
IO6.62 

107.56  °'94 

108.50  °'94 

109-43  I 

110-35  I'H 
111.27 

112.19  °'92 

113-09  0'9° 

114.00  °'91 

I  4.89  °-89 
v  0.90 

i  TC  in 

0.88 

0.88 
0.88 
0.87 
0.87 
120.17  „  «A 


"*s 


si4 


a 


128.59 


0  82 

: 
a 


I35-83 
136.62 


82.10 
83-21 
84.32 
85.42 


.08 


04 


88.68 

89.75 
90.81 
91.86 

93-95 
94.98 
96.00 

98.03 

99-03 
1 00.02 
101.01 

102.96 

103-93 
104.89 
105.84  "'" 
106.79  °'9S 

"    0.94 


109.59  r 
110.51 

'"•43  °:9; 

II2-34  „ 


"5-93  0.88 
116.81 
"7-69  !•" 


I27'83 


129.46 

S 

' 


is? 


i 

0.79 


137-37 


83-30 
84.42 

85-53 
86.63 

88.80 
89.88 

90.94 
92.00 

93-05 


96.16 
97.18 

99.19 
100.19 
101.17 
102.15 


°'98 


106.95  °'94 
107.11  °'94 

108.82 

109-75 
1 10.67 

"1-59 
112.50 

113.40 
114.29 


0.93 
0.93 


0.90 


o 
°0.T7 


I  I6.O7 

117.82 
118.69  ""£ 

"9-55  I 
120.41 

121.26  °-8S 
0.85 

122  05  °'84 

:ss  °;« 

125-45  °'.3 


127.9 

I28.fi 


131.91 


°-79 


136.58 


138.11 


°-77 

°'77 
0  ,0 


60 
61 
62 
63 
64 

65 
66 
67 
68 
69 

70 
71 
72 
73 
74 

75 
76 
77 
78 
79 

80 
81 
82 
83 
84 

85 
86 
87 
88 
89 

90 
91 
92 
93 
94 

95 
96 
97 
98 
99 

100 
101 
102 
103 
104 

105 
106 
107 
108 
109 

110 
111 
112 
113 
114 

115 
116 
117 
118 
119 

120 


12 


TABLES    FOR    THE    TRUE    ANOMALY. 


M 


e  =  .15 


e  =  .16 


.17 


e  =  .18 


e  =  .19 


e  =  .20 


e  =  .21 


M 


120 
121 
122 
123 
124 

125 
126 
127 
128 
129 

130 
131 
132 
133 
134 

135 
136 
137 
138 
139 

140 
141 
142 
143 
144 

145 
146 
147 
148 
149 

150 
151 
152 
153 
154 

155 
156 
157 
158 
159 

160 
161 
162 
163 
164 

165 
166 
167 
168 
169 

170 
171 
172 
173 
174 

175 
176 
177 
178 
179 

180 


'33-48 
'34-31 
'35-H 


140.86 

0.81 


0.8o 


'44-87 


0.7g 


1SJS  - 
AS  ::;,* 


'55-06 
155.83 


157-37 


161.19 


164.99 

165.74 
166.50 
167.25 
168.01 

168.76 

170.26 
171.02 


0.77 
0.76 
0.77 
0.76 
0.76 

0.76 
0.76 
0.76 
0.76 
0.76 

0.75 
0.76 
0.7S 

0.75 

0.75 
0.75 
0.76 


174.02 
174.76 
I75-5I 
176.26 
177.01 


0.75 
0.75 


179-25 
iSo.OO 


135-92 

'36-73 
'37-54 


' 


-       0.8o 
'39-15  0.8I 
'39-96  °- 
'4°-75  ° 


I43.I4 
143-93 
144.71 
I45-50 

146.28 
147.06 
147.84 
148.61 
I49-38 
150.16 
150.93 


I53-23 

153-99 
I54.76 
155.51 


0.79 

0.80 
0.79 
0.78 


o  78 
°'  8 
°'  If 
°'77 


.77 


0.,6 


>-75 
).76 


15778 
158.54 


161.54  07, 
162.29 
163.03   °'74 
I63-78       ™ 


0.74 


'6«-3  ::7; 
168.97 

l69-7i  o;74 


°-74 

0.74 


171.18 
171.92 

172.66 
173-39 


175-60 
176.33 
177.80 

S:"  °-74 
0.73 

180.00 


°-V3 


135.07 
'35-88 
136.68 


14  -uu  0.79 

0.78 
o.  78 

l£  ™  °-7« 


146.88 

I47-65 
148.42 
149.18 
149.94 

150.70 


0.77 


153.72 

154-47 
155-22 


159.67 
160.41 
I6I.I5 

161.88 
162.62 

163.35 
164.08 

165.54 
166.27 
167.00 
167.72 
168.45 

169.18 
169.90 
170.62 


172.79 

'73-52 


0.74 
0.73 

0.74 


0.73 
0.73 

0.73 
0.73 

0.73 
0.73 

0.72 


0 

°  73 


'75-68  °;72 
176.40 

177.12  °"72 

177.84  °'72 

178.56  °'72 

179.28  °-72 
0.72 

180.00 


142.13 
142.90 

143.67 
144.44 


0.79 
0.78 
0.78 

0.78 
0.78 
0.78 
0.77 
0.77 

0.77 
0.76 
0.76 
0.76 
0.76 

0.75 


147-48 
148.23 
148.98 
'49-74 
150-48 


152.72  "-13 

153-46  0;74 

'54-93  0 
155.67  ',, 
156.40  °'73 
157.13 


157-86 


°'73 
°'73 


I59-32  °'73 
160.05  °'73 

l6o-77  °0H 
161.49    ' 
*  0.72 

162.21 
162.94  °"73 
163.66  °'72 


111 

169.38 
170.09 
170.80 


0.72 


172.93 

'73-64 


0.71 

).7I 
).7I 


176.47 
177.17 
177.88 

178.59 
179.29 

iSo.OO 


136.62 


138.95 
139-73 
140.50 
141.27 

142.80 
I43-56 

I44-3I 
I45-07 


„ 

0.78 


°'7 


'      O  75 

'47-32  Q  7* 
148.06 
148.80  °'74 
149-54  °'?4 


'53-94 
154-67 


" 


158.27 

158.99 
I59-70 


161.83 

162.54 

163-25 
163.96 
164.66 
165-37 


71 


°-70 


167.47 
168.17 
168.87 

169-57 
170.27 
170.97 
171.67 
172.36 


0.70 
0.70 


174-45 
I75.I4 
175-84 

176.53 
177.23 
177.92 
178.61 

180.00 


l 


137-37 

139-68 
140.44 

I4L95 


144.20 

144-95 
145-69 
146.43 
147.17 
147.90 

148.63 
149-36 


07S 
7f 

H 

0.7S 


I5I-54 
152.26 
152.98 
153.70 


; 


. 


I57-96  °'7° 

158.67  °;7^ 

'59-37  0  „ 
160.07  °-7° 
160.77  °'7° 
161.47  °-7° 

162.17  °-r 

'  0.69 
162.86 

Tfil    Cfi    °-'° 


167.71 
168.39 
169.08 

16977 

170.45 
171.14 
171.82 
172.50 


180.00 


0.68 
0.69 
0.68 

0.69 

0.68 
0.68 
0.69 
0.68 

0.68 
0.68 
0.68 
0.68 
0.68 


I38.n 


140.38 


3 

• 


°'7S 

O.74 

0    4 
7J 


0.73 
0.73 


141.88 
142.63 

143-37 
144.10 
4l84  °'74 

145-57 
146.30 

'47-03  o"« 
147-75  '' 

148.48   73 
0.72 


150.63  •' 

'5'-34  „; 
152.06  Q  ' 

152.76 

153-47 


0.71 
0.70 


« 

'55- 


0.69 
0.70 
0.69 


'59-06 


163.18 


3 


0.67 


169.28 

169.96 
170.63 
171.30 


0.68 


'73-31 


175-99 
176.66 

177-33 
178.00 
178.66 
179-33 
iSo.OO 


°'66 


120 
121 
122 
123 
124 

125 
126 
127 
128 
129 

130 
131 
132 
133 
134 

135 
136 
137 
138 
139 

140 
141 
142 
143 
144 

145 
146 
147 
148 
149 

150 
151 
152 
153 
154 

155 
156 
157 
158 
159 

160 
161 
162 
163 
164 

165 
166 
167 
168 
169 

170 
171 
172 
173 
174 

175 
176 
177 
178 
179 

180 


TABLES    FOR    THE    TRUE    ANOMALY. 


M 


e  =  .22 


=  .23 


e  =  .24 


e  =  .25 


e  =  .26 


e  =  .27 


.28 


M 


0 

1 

2 
3 
4 

5 
6 
7 
8 
9 

10 
11 
12 
13 
14 

15 
16 
17 
18 
19 

20 
21 
22 
23 
24 

25 
26 
27 
28 
29 

30 
31 
32 
33 
34 

35 
36 
37 
38 
39 

40 
41 
42 
43 
44 

45 
46 
47 
48 
49 

50 
51 
52 
53 
54 

55 
56 
57 
58 
59 

60 


o.oo 
1.60 
3.21 
4.81 
6.41 

8.01 
9.60 

11.20 

12.79 


20.68 


25-35 

26.90 

28.44 
29-97 

33-01 

37-50 
38.98 


4I-92 
43-37 

46.25 
47.68 
49.09 
50.50 

53-28 
54-65 

57-37 

60.04 

61-37 
62.68 

63-98 

66.55 
67.82 
69.07 
70.32 
71-56 

72.79 
74.00 

75-21 
76.41 

77-59 

79-93 
81.09 
82.24 
83-38 
84.51 


A 
.60 
.61 
.60 
.60 
.60 


-58 

•  57 

•  55 

•  54 

•  52 


•*> 

;» 


" 


33 


.25 
.24 
•  23 

.21 
.21 

.20 


II 


O.OO 


8.20 

9-83 

11.46 

13.09 
14.71 

16.33 


21.16 
22.76 

24-35 
25-93 
27-51 
29.08 
30.64 

32.19 

33-73 
35-27 
36.79 
38-31 
39.82 

42.80 
44-28 
45-75 
47-20 
48-65 
50.08 


55-71 
57-09 

58-45 

61.15 

62.49 
63-81 
65.12 
66.42 

67.71 


70.25 
7I-50 
72-75 

73-98 
75-20 
76.41 
77.61 
78.80 

79-98 
81.15 
82.31 
83.46 

85-72 


A 

1.64 

1.64 

.64 

.64 
.63 

-63 


62 


39 


•* 


.. 
-34 


.29 


23 


O.OO 


'"68 

3-36  [. 


1.68 


1.68 
1.67 

1.67 
"•2   '£ 


20.01 


ii 


32.91  ,  „ 

3 


4°-67  ,.s 


3 


53-96  [ 

St!  3 

_o  ¥_    1-39 


62.28  i 

64^6  '•* 
66.28  '-3 


68.88 
70.17 


I    27 


73-95 ;;:; 

75.19  T  „ 
76.41 

77-63  •" 
78.83  -2° 

80.02 

1.18 

81.20 


84^68 ;;; 
86.94 ' 


O.OO 

1.72 

3-44 
5-16 
6.88 

8-59 
10.30 

I2.OI 

13-72 


1-72 

- 


MI 


25.48 
27-13 
28.77 
30.41 
32.03 

33-64 
35-24 
36.84 

39-99 

43-09 
44-63 
46.15 
47.66 

49.16 
50.64 
52.11 
53-57 


a: 


•" 


:•:: 
- 


66.12  Ic 

67-45  ' 

68'77  "30 

70-07  i>29 

72.64  ;-2* 

73.91  \ 

75-16  t\,54 
76.40 
77.63  • 3 


1. 17 

I.IS 
I. IS 

1. 12 


82.43 
83.60 

84.75 


o.oo 
1.76 
3-53 
5-29 


12.30 
15-79 


A 

1-77 
1.76 

1.75 
1.75 
1.75 

1.73 
1-73 


26.08 

29.44 
31.10 
32.76 

34-40 
36.03 
37.66 

39-27 
40.86 

42-44 
44.01 


1.66 
1.66 
1.64 

1.63 
1.63 

i. M 


,  „ 
=7 

3 


57-55  . 


60.41 
61.82 

64-59 
65.96 

67-3I 
68.64 
69.97 

71.28 
72.58 
73-86 


1-37 
I.3S 
1.33 

1.31 


77-63 
78.86 
80.08 
81.29 


87.04 
88.16 


85-99 
87.14 
88.27 

89-39 


• 


O.OO 

I.8I 


7.22 

9-O2 
I0.8I 
12.60 

14-39 

17-94 
19.71 

21-47 
23.22 
24.96 

26.69 
28.41 
30.12 
31.82 

35-18 
36-85 


;:  : 

T 

i.  So 


1.77 
1-77 


1-73 


'-70 


43-37 

44.96 

46.54 
48.11 
49.66 

51.20 

52.73 


.  ,. 
•» 

'  * 


1-54 
1.53 


iSS 


65-77  ,  3g 

^s'  ;•* 

69.85  '34 

71.18  ;:33 

£E  - 

i~  ^  1.29 
1.27 


1.25 
78.87 
80.10 
81-32    '•" 


84.91 
86.07 

88^7 
89.50 

9O.62 


'" 


1.14 


O.OO 

1.85 
3-70 

5-55 
7.40 

9.24 
11.08 
12.91 

H-74 


I.8S 
1.85 


1.84 


18.38 
2O.I9 
21.98 
23-77 
25-55 


30.82 


$& 


47-54 
49-13 

52.26 
53-80 
55-33 


1.81 

1.78 

1-77 
1-74 


' 


•  4 
'  " 


62.72 


66.97 
68.35 
69.72 
71.07 
72.41 


1.38 
1.37 
I.3S 
1-34 
1.32 

73-73  ,  3I 
75-04  ^ 
76.33  ! 
77-61  T'28 
78.87 

80.12 


I.2S 


89.62 
90.74 

91.86 


0 

1 

2 
3 
4 

5 
6 
7 
8 
9 

10 
11 
12 
13 
14 

15 
16 
17 
18 
19 

20 
21 
22 
23 
24 

25 
26 
27 
28 
29 

30 
31 
32 
33 
34 

35 
36 
37 
38 
39 

40 
41 
42 
43 
44 

45 
46 
47 
48 
49 

50 
51 
52 
53 
54 

55 
56 
57 
58 
59 

60 


TABLES    FOR    THE    TRUE    ANOMALY. 


M 


.22 


e  =  .23 


.24 


.25 


.26 


.27 


e  =  .28 


60 
61 
62 
63 
64 

65 
66 
67 
68 
69 

70 
71 
72 
73 
74 

75 
76 
77 
78 
79 

80 
81 
82 
83 
84 

85 
86 
87 
88 
89 

90 
91 
92 
93 
94 

95 
96 
97 
98 
99 

100 
101 
102 
103 
104 

105 
106 
107 
108 
109 

110 
111 
112 
113 
114 

115 
116 
117 
118 
119 

120 


84.51 
85-62 

86-73 


90.00 
91.07 

93-20 
94.24 

95-28 
96.31 
97-33 

99-35 


.07 


.04 


.00 

0.99 
0.98 
0.98 


107.12  °-94 

108.06  °'94 
108.99      93 

V   0.93 
109.92 

JJ°-84  I'll 

"3-55  o.^ 

"4-45  o^g 
"5-33  0.88 

»™  "" 

117.96  °' 

118.82 
119.68 


122.22 

123.06 
123.89 


0.86 

0.86 
0.85 
0.85 
0.84 
0.84 


127.17 

33 


0.82 
0.82 
0.81 

0.81 
0.80 
0.80 
0.79 
0.79 

0.79 
0.78 


U 

137.34 


138.85 


°  I. 

°0.1S6 


8572 
86.84 

87-95 
89.04 

91.21 
92.28 
93-34 
94-39 
95-43 

96.47 
97-49 


99-52 
I00'52 


'03-47 


.02 
.01 

.00 


0.93 

1^09    °'92 
*    0.92 

III.OI 

"if,  a 
::ss  a 


II9-82  Og« 

I2a67  o  S! 

I2i-s'  ::  : 

122.35  ° 

I23-'8  0.82 


124.00 

-  § 


128.06 
128.86 


I32-00 


0.77 


-» 


0.74 


86.94 
88.05 
89.16 
90.26 
91-34 


94-54 
95-59 

97.66 

98.68 

99.69 
100.69 
101.68  °'99 

0.99 


0.97 


10747 
IO8.4I 


.01 

.00 


120.80 


0.91 


''477  "•!! 

115-65  0;87 
116.52 
''7-39  0;86 

!„..    0.86 


„  g. 


0.78 
0.76 

0.77 
0.76 
0.75 


124.94 


132.82 


139-57 


137-34 
138.08 
138.82 
139.55 
140.28 


88.16 
89.28 


1.09 


94-69 

95-74 
96.78 
97-82 

98.84 

99-85 
100.86 
101.86 


106.70 
-7-65 


IIO-44 


O.02 


26  °'91 
0.90 

113.16 

T  T     ne   O.o9 

"4^3  °'g8. 
115-81  °-f 

1 16.68  °'*7 
0.87 


"343  • 

:ss  a 


129.81 

'30-58 


132.88 

I33.64 
134-39 
I35.I4 
135-88 
136.62 

137.36 
138.09 
138.82 

139-54 
140.26 

140.98 


; 


°'73 


89.39 
90.50 
91.60 

93-77 
94.84 
95-90 
96.94 
97.98 
99.01 

IOO.O2 

102.03 
103.02 
104.00 

104.97  o.po 

Io6%8  °-9S 

107.83  00H 

'77  0.93 

"iS  °-9i0 

"2'43  0:90 
"3-33  0.8p 

114.22 
115.10 
115.98 


.01 
i. 01 

I.OO 
0.99 
0.98 
0.97 


0.88 
* 


0.86 
0.86 

0.8s 


122.74 


0.79 
126.77 
127.56  °-79 
128.35 


a 


129.90 

130.67 
I3I.43 
132.19 

132.94 
I33.69 


o.76 


138.10 

138.82 

139-54 
140.25 
140.96 

141.67 


a 


90.62 
91-73 

93-91 

94-99 
96.05 
97.10 
98.14 
99.17 
100.19 

IOI.2I 
102.21 


08 


' 


106.12 

O.Q5 
IO7.O7 

108.01  °'94 

inS  nc  °'94 


I  IO.8O 
III.7I 
II2.6I 


°-90 

a 


"9-57  0.84 


I23-7° 


g, 


£4.5j  — 

126.89 
127.68 


79 

0.79 


133-02 


a 

™" 

a 


I374I 

138.84 
139-55 
140.25 


o    o 

°- 
0.70 


91.86 
92.96 
94.06 

96.20 

97.26 

98.31 

99-34 

100.37 

102.39 
103.38 
104.36 


.06 


03 


107.26 

108.20  °'94 

109.14  °-94 

118.06  °-9J 


\\lfo 


"5-46 


0.87 


118.90 
119.74 

120.57 
121.40 

122.22 


I24-65 


0.83 
* 


133-10 
133-83 
134.56 
I35.29 
136.01 
136.73 


0.74 
0.7S 


i42-35 


138.56 
140.26  °-7° 
140.96  0'7° 

ili  (U  °  9 

0.68 
0.69 

143.02 


60 
61 
62 
63 
64 

65 
66 
67 
68 
69 

70 
71 
72 
73 
74 

75 

76 
77 
78 
79 

80 
81 
82 
83 
84 

85 
86 
87 
88 
89 

90 
91 
92 
93 
94 

95 
96 
97 
98 
99 

100 
101 
102 
103 
104 

105 
106 
107 
108 
109 

110 
111 
112 
113 
114 

115 
116 
117 
118 
119 

120 


TABLES    FOR    THE    TRUE    ANOMALY. 


M 


e  =  .22 


e  =  -23 


.24 


e  =  .25 


e  =  .26 


.27 


.28 


M 


120 
121 
122 
123 
124 

125 
126 
127 
128 
129 

130 
131 
132 
133 
134 

135 
136 
137 
138 
139 

140 
141 
142 
143 
144 

145 
146 
147 
148 
149 

150 
151 
152 
153 
154 

155 
156 
157 
158 
159 

160 
161 
162 
163 
164 

165 
166 
167 
168 
169 

170 
171 
172 
173 
174 

175 
176 
177 
178 
179 

180 


139-59 


'42-55 
143.29 


0.74 
0.73 

0.74 
0.73 
0.72 

'^  °0.H 
146.19 
146.9,  °-'2 
14762  °'71 

$33  :•:; 
,49.04 
*  0.71 

149-75 . .. 
,50.46  °-y^ 

,5,!86  °-7° 
'52.56  °'?° 


\y.  y.  0.68 

158.08  °'£9 

159-44 
,60.12 

,60.79  °-67 

,61.47 

,62.14 

,62.82 
0.67 


I64'83  o'o6 

iSue  °-67 
0.67 

,66.83  „ 

l67-49  °'£ 
168.16  °'67 
168.82  °-°° 

'69-48  *2 


'71.46 
«?»•» 

'7-78 


T-f 


,76.07  *T° 
'    o.6s 

l~j\a   °-66 

;£g  °:" 

•«•«  « 

,80.00 


139-57 
,40.30 

,41.04 

141-77 
,42.49 


0.74 


141.37 
146.08 


146.79  „ 

!£S  °- 
,48.90  °-7° 

,49.60  °-7° 
0.70 

'5°-3°  0.69 

;^:H  -* 


'53-74 


0.6g 


'56-46 


159-15 
159-82 

,60.48 


,67.07 

,67.72  o-6* 

168.37 


°-6s 


171.62  °-s 
°-6s 


O.O5 

11 

*   0.6s 

0.64 
0.64 

,78.7,    °'64 

•79-36  °;6* 
,80.00 


,41.00 
,42.44 


0.72 
0.72 


145-99 
'46-69 


'48-77 

'49-46 


153-54 
,54.22 
154-89 


,60.84 


'^•79 

'63-44 


0.66 

o.6s 
0.65 
0.6s 


0.6s 


166.67       e 

I 

,7l.?4  °'^4 
171-78  °t 


'73-68 
'74-31 


A 
0.71 


150.01 

'50-68 


ill 

,61.19 
,61.83 
,62.47 
,63.11 
163.75 


165-65 
166.28 


l&%   *«3 

,68.80  °-°3 


170.68 


'7-55  ~ 
'73-1?  0.03 

|1 

,76.90 
I77-52 
178.14 
,78.76 
I79-38 


0.62 
0.62 


Hi 

0.67 


157-72 
158.36 


o  66 


s 


064 


162.79 


,69.01 
,69.62 


180.00 


180.00 


,72.08  ° 
,72.69  °-*r 

'73-30  a 

II 

'76-96  O6r 

177-57 

,78.18 

,78.78 

'79-39 

180.00 


'43-72 


1 


1 


160.01 
160.63 
161.25 

161.87 
162.49 


° 

* 


166.78  °-*r 

167.39  °;£j 

,68.00 

168.60  °-6° 

,69.21  "-*1 

,69.81  °-60 

170.42  «•«' 
0.60 


,72.82 


1  74.02 
'74.62 


177.01 


O.S9 
0.60 


,78.8, 
,79.40 

I8O.OO 


0.68 
0.68 

0.67 


145-71 

146.38 
147.04 
147.70 
148.36 
149.02 

149.67 
150.32 
150.96 
I5I.60 

152.88 
I53-52 


o.6s 


5 

'58-53 


0.63 
0.63 
0.63 


° 


,59.76  °-62 
,60.37  °'61 
160.98  °'61 

,6,  S9  ° 

"  0.6 1 

,62.20 
,62.81  °6' 
163.42 
,64.02 

,6l62  °-'° 
0.6 1 


166.43 
167.02 
167.62 

168.22 

168.81 
169.4, 

170.00 

170.59 
171.18 

171.78 
172.37 
172.95 

'73-54 


0.60 
0.59 


175-31  °-59 
I75-90 

176.48  °'f* 

177.07 
,77.66 
178.24  °-ss 
178.83  °'59 
179.41   5 

0.59 
iSO.OO 


120 
121 
122 
123 
124 

125 
126 
127 
128 
129 

130 
131 
132 
133 
134 

135 
136 
137 
138 
139 

140 
141 
142 
143 
144 

145 
146 
147 
148 
149 

150 
151 
152 
153 
154 

155 
156 
157 
158 
159 

160 
161 
162 
163 
164 

165 
166 
167 
168 
169 

170 
171 
172 
173 
174 

175 
176 
177 
178 
179 

180 


i6 


TABLES    FOR    THE    TRUE    ANOMALY. 


M 


.29 


e  =  .30 


e  =  .31 


-32 


-33 


-34 


-35 


Jlf 


0 

1 

2 
3 
4 

5 
6 
7 
8 
9 

10 
11 
12 
13 
14 

15 
16 
17 
18 
19 

20 
21 
22 
23 
24 

25 
26 
27 
28 
29 

30 
31 
32 
33 
34 

35 
36 
37 
38 
39 

40 
41 
42 
43 
44 

45 
46 
47 
48 
49 

50 
51 
52 
53 
54 

55 
56 
57 
58 
59 

60 


a 
o.oo 

1.90  '-90 

II  is 

1.89 


13-24 


18.83 

20.68 
22.52 

26.17 


29-77 
31-55 
33-32 
35-07 
36.81 

38.53 
40.24 


I'll 
'g3 

, 
i.  80 


7 


I.7O 


57-97 


- 

u 

" 


1.48 
1.46 

1.43 

1.41 


6O.07 


\J     S 

65.35 
66.78 

68.19 
69.58 

70.95 
72.31 

73-65 
74.98 

77-59 
78.87 
80.13 

81.38 
82.61 
83-83 


87-41  ,  I7 

88.58  '  7 

89.73 

90.86  I>13 

91.99  «-13 

y  i. ii 

93.10 


i.  23 


o.oo 
1-95 
3-89 

5-84 


13-57 
15-49 
17.40 

19-30 
21.19 


24.94 
26.80 

28.64 


54-44 
56.02 

57-58 
59-12 
60.65 

62.16 

65.12 

66.57 
68.00 

69.42 
70.82 
72.20 
73.56 
74-91 
76.24 

77-55 
78.85 
80.13 
81.40 

82.65 
83.88 
85-10 
86.31 
87.50 

88.67 
89.83 
90.98 


94-34 


A 

1.95 
1-94 
1. 95 


32.29 
34.10 
35-88 

37-66 
39-41 
4I-I5 
42.87 
44-58 

46.27 
47-94 
49-59 


1.91 
1.90 

1.89 

1.88 
1.87 
1.86 
1.84 

1.83 
1.82 
1.81 


i.7S 
*•" 


I.S6 
I-S4 
I. S3 

LSI 

1.48 
1.48 

1.43 

1.42 

1.40 
1.36 


1'27 

I.2S 


1.22 
1. 21 


•17 
.16 


O.OO 
2.OO 


1.98 


15.88 
17.84 

19-79 
21.72 

23-64 


31'21 
33-06 
34-90 


40.32 
42.09 
43-84 

45-57 
47.28 

50.66 
52.31 
53-95 


I.9S 


'13 


S 


66.34 
67.80 

70.67 
72.07 
73-46 
74-83 

77-51 
78.83 
80.13 

82.68 

83-93 
85-16 
86.38 
87.58 

88-77 

89-94 
91.09 

92.24 
93-37 
94-48 

95-58 


I.2S 


•  IS 
-IS 


o.oo 

2.05  2'os 

4.10  2'°s 

6.14  2'04 

8.18  2'04 
2.04 

10.22 

12.25    2'°3 
0    2.02 

2. 02 


. 
18.29  2- 

*  1- 


99 


3:3  - 


- 

*"••»  1.86 

37-59  * 


> 
5°-°4   7 


56.71 
58.33 
59-92 
61.50 

63.05 

64.58 
66.09 
67.58 


1-55 
I. S3 

LSI 


70.50 
71-93 


j  ,„ 


77.46 

78.80 
80.12 
81.42 
82.70 


1.30 


85.21 
86.44 
87.66 
88.85 
90.04 

91.21 


I.I7 


93-50  • 
94.62  • 2 

95-73  ,;„„ 
96.82 


o.oo 

2.10 

4.20 
6.30 
8.40 

10.48 

12.57 
14.64 

16.71 
18.76 

20.80 

22.83 
24.84 
26.84 

28.83 
32.74 

34-68 
36.59 

40.35 
42.20 

44-03 


49.40 

. 

5I-I4 

52.86 


57.89 
59-52 
61-13 
62.72 
64.28 

65.82 
67-34 


A 

2.10 


2.08 


2'°s 
2.04 


1.96 
L95 


£3 !:S 

1.43 
73-21 


77.40 
78.76 

80.10 
81.41 
82.71 


1.34 


86.50 

87.73 
88.94 


92.48 
93.63 
94-76 

95-88 
96.98 

98.07 


1.24 
1.23 

1. 21 
1.20 


I. IS 

1. 13 


O.OO 
2.16 


2.16 


8.62 

10.76 
12.90 
15.02 
17.14 
19-25 

21-34 
23-41 
25-48 
27-52 
29-55 


2.14 

2.14 

2.12 


SS 


3.O9 

2.07 

2.O4 
2.OI 

1.99 
1.97 
I.9S 


1.90 
I''?'    !••» 


1.79 


46.89 
48.70 

50.49 
52-26 
54-00 


59.08 
60.73 
62.36 
63.96 

67.08 
68.61 
70.12 
71.61 


'-60 


'•" 


74-51 
75-93 
77-33 
78.71 
80.07 

81.40 

82.72 


1.30 


87.80 
89.03 
90.24 

91-43 
92.60 

93.76 
94.90 
96.02 


99.31 


1.24 


1.16 
1.14 

1. 12 


O.OO 
2.22 

4-43 
6.64 

8.85 


I5-42 
17-59 

21.89 
24.02 
26.13 
28.22 


A 

2.22 


36.39 
38.38 
40-34 

42.28 
44.20 
46.09 

47-95 
49-79 
51.61 
53-40 
55-i6 


2-13 


1.94 


63.60 
65.22 
66.80 

68-37 
69.91 
71.42 
72.91 
74-38 
75-82 

78^5 
80.03 
81.39 

82.72 
84.04 

85-33 
86.61 

87.87 
89.11 


1.  57 


92.72 

95-04 
96-17 
97.29 

98.39 
99.48 

100.55 


1.22 
1.20 
1. 19 


0 

1 

2 
3 
4 

5 
6 
7 
8 
9 

10 
11 
12 
13 
14 

15 
16 
17 
18 
19 

20 
21 
22 
23 
24 

25 

26 
27 
28 
29 

30 
31 
32 
33 
34 

35 
36 
37 
38 
39 

40 
41 
42 
43 
44 

45 
46 
47 
48 
49 

50 
51 
52 
53 
54 

55 
56 
57 
58 
59 

60 


TABLES    FOR    THE    TRUE    ANOMALY. 


M 


.29 


e  =  .30 


e  =  -31 


-32 


-33 


-34 


-35 


M 


60 
61 
62 
63 
64 

65 
66 
67 
68 
69 

70 
71 
72 
73 
74 

75 
76 

77 
78 
79 

80 
81 
82 
83 
84 

85 
86 

87 
88 
89 

90 
91 
92 
93 
94 

95 
96 
97 
98 
99 

100 
101 
102 
103 
104 

105 
106 
107 
108 
109 

110 
111 
112 
113 
114 

115 
116 
117 
118 
119 

120 


93.10 
94.20 
95-29 


97-4- 


99-5  ' 
100.54 


.04 
.03 


.99 


;3?  °:ll 
0.94 


- 


"5.64 
"6-51 


"9-°7 
"9-91 

"0.74 


" 


07 


'      0.70 
130.21 

130-96  °'7S 
°-74 


I27''5 


'36-07  °0\H 
'36-79  0.70 

'S-  :• ; 
138.89  °-6y 

'39-59  0;;9 
140.28 

IffS  "' 

142-33 
143-00 


143-68 


94-34 
95-43 
96-51 
97-58 
98.64 

99-68 
100.72 
101.74 

103.75 


I08'39  o  94  j  I09-52 

mr»  1 1  "•="*     ijr»  «r 


.07 


4 


I05-7I  °'97 

106.68  ° 

IO7.64  °-!X) 

108-58  °'94 

0.94 
0.93 


11045 

1  1  1.  37 
112.28 


°'92 


II4.07 

"4-95 


118.40 
119.24 
I2O.08 
120.91 

122.54 


0.7O 

124.94 

125.73  I'll 
126.51 
127.28  °-77 
128.05  °-77 
128.82 


°'77 


I3°-32 
131.07 

131.81 
132-54 

133-27 


75 


136.85  °o~^o 
137-55  „ 


140.98 


144-33 


fi. 


95-58 
96.67 

97-74 
98.81 
99-86 

100.89 
101.92 


132.65 
133-37 
I34-09 
134-80 


1.03 
1.03 


I04-93 


107.83 
108.78 
109.72 

1 10.65 


°'94 

0.93 


116.88 
117-74 

119-43 


121.08 

121.90 


°-*° 


1313 

128.95 
129.70 


!36-9i  °'7° 
'37-61  o-6p 

:SS  a 

SS- 

141.01 


141.68 


0.67 


0.66 


144-97 


96.82 

97-91 

98.97 

100.03 

102.10 
103.12 
IO4.I2 
105.12 
IO6.IO 

107.07 


0.97 

0.06 


108.03 
108.98  0-9S 
109.92  °-94 


113-57 
114.46 

1 16.21 
117.08 
"7-93 


120.44  o 
121.26  °'82 
122.08  ° 


s*  a 

126.04 
126.81  °;77 


'30-57 


0.7 


'33 


'4'-05 


!JS?  - 

144-31 
144.96 

145-60 


s 


98.07 
99-14 

IOO.2O 
101.25 
IO2.29 


107.27 

'   '  0.96 

108.23 
IO9.I8 


111.05 
111.97 

112.88 


°'94 

°'93 

°-92 

0.91 


0.86 
0.86 


119.80 
120.63 

121.45 


123.86 

-4-65 


'  0.77 
I26-20  o  „ 
I26'97  o  70 


0.7S 
I29'23  0.74 
129-97  o  74 

J30-7I  o.7,4, 

I32'i6  °'72 
0.72 

132.88  n 


137.07 


a 


146.22 


loTX  '- 

'02"»7 |;° 


as  a 


',SS  -- 

'"£  °:E 

113-98  „ 


'4 


"5-75 
1 16.62 
117.48 

"8-33 
119.17 


124.04 


127.89  °-76 
128.64  °'7S 
129.38  °'74 

0.74 
130.12 

130.85  ° 

131-57  o  H 
132.29      ' 
133-00  * 


139-17 

'39-83 


°1S 

- 


'43-07 


'44-97 


146.83 


0.62 


100.55   J06 
101.61   *•*• 

%S  '°°> 

'°4-7i  l'°* 


107.68  ° 
108.64  ° 

109.59  °;9s 

"0-54  o 
'"•47  0^2 

!ES  4 


0.89 
115.08 
115.96  °-" 
116.83  „ 


0.83 

° 
°-8* 

; 

0.80 


"9-37 

120.20 
121.02 

I2'-84 

I22-64 


128.80 

'29-54 


131.00 

£5 


33  - 

1%%  "* 


141.20 

33 


'44-37 


147-43 


60 
61 
62 
63 
64 

65 
66 
67 
68 
69 

70 
71 
72 
73 
74 

75 
76 
77 
78 
79 

80 
81 
82 
83 
84 

85 
86 
87 
88 
89 

90 
91 
92 
93 
94 

95 
96 
97 
98 
99 

100 
101 
102 
103 
104 

105 
106 
107 
108 
109 

110 
111 
112 
113 
114 

115 
116 
117 
118 
119 

120 


i8 


TABLES    FOR    THE    TRUE    ANOMALY. 


M 


e  =  .29 


e  =  .30 


.31 


.32 


e  =  -33 


-34 


-35 


120 
121 
122 
123 
124 

125 
126 
127 
128 
129 

130 
131 
132 
133 

134 

135 
136 
137 
138 
139 

140 
141 
142 
143 
144 

145 
146 
147 
148 
149 

150 
151 
152 
153 
154 

155 
156 
157 
158 
159 

160 
161 
162 
163 
164 

165 
166 
167 
168 
169 

170 
171 
172 
173 
174 

175 
176 
177 
178 
179 

180 


~t*J'v 

!SS  £ 


335 


iil 

!SS  °-«° 
160.73 

161.33 
161.93 


iss 

166.68 
167.26 

''7.85 


°-s8 


*» 

166.60  °-58 
176.18  °-s8 

'70-77 


171.35 
171.93 

173.09 
173.66 

174.24 
174.82 
175.40 
175.97 
176.55 
177.12 
177.70 
178.27 
178.85 
179.43 
180.00 


0.58 

° 


0.57 
0.58 

0.58 
0.57 


I44-33 


'46-93 


° 


: 

°-*4 

< 


148.86 
149.49 
150.12 

!S3  2 

!$?•£  ol 


'53-86 


0.62 

ii.fn 


ss 


5 


160.49  °-f 

161.09  ° 

161.68  °-» 
162.26  °-58 

0.59 
162.85 

!&£  *S 

0.58 


166.34  °'H 

166.92  °ol8 

167-50  °'*8 

i68-°7  05l 

168.65 

169.22  °'S7 

169.79  ° 
170.37   '„ 

170.94 

*  0.57 


172.64 
173.21 
173.78 

174.35 


6 


0.57 


0.57 


. 


178.87 
17944 

iSo.OO 


146.25 
146.89 
147-53 
148.16 
148.79 
14942 


153.12 

'5^73  ;;6; 

:ss  ~ 


°0;f0 


157-33 
157-92 
158.51 
159-10 

159-69 
160.27 

161.43 
162.01 

163.17 

164.32 
164.89 


0.58 
0.58 
0.58 


°0  " 
°'s8 


0*7 

Hi 


171.66 
172.22 
172.78 

'73-34 
'73-90 


176.67 

177-23 
177.78 

178.34 
178.89 

179-45 
180.00 


0.60 
0.60 
0.59 

'55-40  °06S°9 
'55-99  0;S8 
156.57  0  ' 

157-16  o;** 
157-74  0-so 

158.91  °'s8 
159-48  ° 
160.06  **• 

160.63 

161.20  »•" 

161.77  °- 


163-48 
164.04 
'64-60 


166.29 
166.84  "•" 
167.40  °'s° 

f    f  O.  SO 

167.96  * 


170.72  I'll 

171.82 
172.91  °'S4 

173.46  °' 
174-01  0'H 

'74-55  0 
175-10  '" 

175.65  o 
176.19  °-*4 

177.28 
177.82 
178.37  o 

178.91 
179.46 


180.00 


0.54 


146.22 

146.84  °-6i 

147.46  °'  2 

148.08  0-;"2 

148.70  C     * 
o.oi 

'49-31 
149-92  „ 


ill 


'55-27 


0.59 

0.58 
0.58 
0.57 

0.57 


160.99 


0.57 

0.56 
0.56 


162.67 

163.78 
164.34 


Igg  « 

18:8  - 


°-54 

0-54 


174.12 
174.66 
175.19 

176.80 

177-33 
177.86 
178.40 
178.93 
179-47 
180.00 


• 


0.54 


146.83  u 

147.44  °'fi' 

148.05  0-*r 

148.66  °'" 

149.27  °'*Q 

140.87 

*  0.59 

I5i!o6  °'60 

TCI  fit  °-S9 


0.59 


152.83 

'53-41 
153-99 


•la 


0  „ 
57 


158.55 
159-12 

I59.67  - 
160.23  °' 
l6O.79  ° 

ly  0.55 
161.34  0 
161.89 
162.44  °' 
162.99  ° 

163-54  °; 


165.17  °-S4 
165.71  l\H 

0.54 
166.79 

!g:38i  o- 


170.53  o  „ 
171.06    OJ 

171.59  I'll 

172.12 

172.65  °'S3 

,1,  ¥o   0-S3 


17476 

!?3:S  °- 
176.33  „ 

'76-86  »;« 

'77-38  0  S2 
177.90 

'78-43  I'll 
178.95  „ 
179.48  Q 

180.00 


147-43 
148.04 

'48.6? 

'49-|3 
'49-83 


151.00 


'53-32 


O.s8 

° 


0    8 

::  ; 


3 


168.61 


159-50 
160.05 


S 


161.68 


162.77 
163.30 

164.38 
164.91 

165.97 


: 


°'S2 


0S2 


I73.30 
173.82 

174-34 

I74.85 
175-37 
175-88 
176.40 
176.91 

177-43 
177-94 


• 


. 


0.51 
0.52 


180.00 


120 
121 
122 
123 
124 

125 
126 
127 
128 
129 

130 
131 
132 
133 
134 

135 
136 
137 
138 
139 

140 
141 
142 
143 
144 

145 
146 
147 
148 
149 

150 
151 
152 
153 
154 

155 
156 
157 
158 
159 

160 
161 
162 
163 
164 

165 
166 
167 
168 
169 

170 
171 
172 
173 
174 

175 
176 
177 
178 
179 

180 


TABLES    FOR    THE    TRUE    ANOMALY. 


M 


e  =  .36 


e  =  .37 


.38 


-39 


-4° 


.41 


.42 


M 


0 

1 

2 
3 

4 

5 
6 
7 
8 
9 

10 
11 
12 
13 
14 

15 
16 
17 
18 
19 

20 
21 
22 
23 
24 

25 
26 
27 
28 
29 

30 
31 
32 
33 
34 

35 

36 
37 
38 
39 

40 
41 
42 
43 
44 

45 
46 
47 
48 
49 

50 
51 
52 
53 
54 

55 
56 
57 

59 
60 


O.OO 

2.28 

4-55 
6.82 


15-84 
18.06 
20.27 

22.47 
24.65 
26.81 
28.95 
31-07 

33-17 
35-24 

39-31 
4I-3I 


2.21 
2. 2O 

2.18 

2.14 


I.9S 

"  * 


49-5 


52-76 

54-57 
56-36 
58.12 

59-85 

6i-55 
63-23 

64.88 


3 


69167 
71.21 


75-70 

77-15 
78.58 
79.98 
81.36 
82.71 

84-05 
85-37 
86.66 


90.42 


96.32 

97-45 
98.56 

99-65 
100.73 

101.80 


I.4S 


1.34 


• 


'  3 


0.00 

2.34 
4.68 
7.01 

9-34 
11.66 


2'34 
2'33 


SB 


2.25 


25-30 

27-5I 
29.70 
31-86 

34-01 
36.12 
38.21 
40.28 
42-31 

44-32 
46.30 

50-18 
52-07 


57-58 
59-35 
61.10 

62.82 
64.51 
66.17 


2.19 
2.16 

2.IS 
2. 1 1 

2.07 
2.03 

2.OI 


UJl 


I.SS 

£5  ;-s 

75-57  H° 


78-49 
79.92 

82.70 
84.06 

85.39 
86.70 
87.99 


.-43 


1-33 


97.60 

98.72 

99.82 

100.91 

101.98 

103.04 


1.  13 


O.OO 

2.41 
4.81 

7-21 


A 

2.41 
2.40 
2.40 


11.98 

33! 
35 


2.31 
2.28 


ss 


43-35  2;, 

45-39  2 

47-40  ' 

49-38  ' 


55-  I4 
57'00 

SS 


64.11 


I-S9 


75-42 


82.68  i-4 


86.74 
88.04 
89-33 
90-59 
91.84 

93.06 
94.26 


1.33 
1.30 


98.89 

100.00 

101.09 

103.23 

104.28 


O.OO 

2.47 

4-94 
7-41 


17.18 
19-58 
21-97 

24-33 


44.41 
46.48 


76.78 
78.29 
79-77 
81.22 
82.64 


2.47 

2.47 


2.40 

2.36 

2.34 
2.32 


S  S 

33-54 


;:;; 
:: 

2.07 


56.37 
58-25 
60.09 


4 


65-43  , 


1.53 
1.51 
1.48 
1.45 

1.42 


85.42  ' 

86.77 

1.32 

88.09  , 


93-17 

94-39 
95-58 
96.76 

97-91 

99-05 

100.17 

101.27 

102.36 


1.24 

1.22 

1. 19 
I.I8 

I. IS 


I. 10 
1.09 
1.07 

1.03 


105-51 


O.OO 

2-55  2 

5-09  . 

7-63  , 

IO.I5 

a   2.52 

12.67 

TC  ti    2's° 


2°''3 


' 


•* 


29-77 
32.11 

34-43 

36-71 
38-95 

43-35 
45-50 


, 

4 


2 

53-73 


90 


ss 


78.17 


82.60 
84.02 

8S-42 
86.79 
88.13 

J 


*••* 


I>34 

1-33 


90-75 
92-03 


94-51 


1.23 
i. 21 
95-72 
96.90     '  ' 
98.07  I'17 


101.45 

102.55 
103.62 
104.68 
105.72 

106.75 


1.07 

1.06 
1.04 
1.03 


O.OO 
2.62 


-•45 


32? 

18.16 
20.70 


••" 


3°-58  2;« 


35-34 


42.22 
44.44 
46-63 

48.77 
50.88 

52.95 
54-98 
56-97 

58-92 


64-56 
66.36 

68.13 


83-99 
85.41 
86.81 
88.17 
89-51 


S 

I.9S 


1.77 


76.46 
78.03 

79-57 
81.07 


93-38 
94-63 

97-05 

98.23 

99-38 

100.52 

101.64 

102.74 


104.88  I'° 


106.96  *'°3 

I.OI 

107.97 


i.  60 

I.S7 


I-SO 


'•« 
1.32 


1.22 
1. 2O 

I.IS 
I.IS 

1.14 

I. 12 
I.IO 


O.OO 


'8.69 


26.41 
28.93 
3I-42 
33-87 


2.S8 

2.S4 
2.49 


38.66 
4I.OO 
43-30 
45-56 
47.78 

49-96 
52.10 

54-20 


92.20 
93-49 

94-74 
95-98 
97-19 

98.38 
99-55 


2'34 


4 


60.24 
62.18 


1-97 


71.26 

72-97 
74.64 
76.27 

77-87 
79-44 


88.20  ''3 


1.24 

1. 21 

1. 19 

1. 17 
I.IS 


IO4.O2 
105.09 
IO6.I4 
IO7.I8 
IO8.2O 

IO9.20 


0 

1 
2 
3 

4 

5 
6 

7 

8 
9 

10 
11 
12 
13 
14 

15 
16 
17 
18 
19 

20 
21 
22 
23 
24 

25 
26 
27 
28 
29 

30 
31 
32 
33 
34 

35 
36 
37 
38 
39 

40 
41 
42 
43 
44 

45 
46 
47 
48 
49 

50 
51 
52 
53 
54 

55 
56 
57 
58 
59 

60 


20 


TABLES    FOR    THE    TRUE    ANOMALY. 


if 


.36 


e  =  .38 


-39 


.40 


.41 


.42 


if 


60 
61 
62 
63 
64 

65 
66 
67 
68 
69 

70 
71 
72 
73 
74 

75 
76 
77 
78 
79 

80 
81 
82 
83 
84 

85 
86 
87 
88 
89 

90 
91 
92 
93 
94 

95 
96 
97 
98 
99 

100 
101 
102 
103 
104 

105 
106 
107 
108 
109 

110 
111 
112 
113 
114 

115 
116 
117 
118 
119 

120 


101.80 
102.85 
103.88 
104.90 
105.91 

106.90 
107.88 
108.85 
109.81 
110.75 


115-30 
116.17 


I-°S 


1. 01 

0.99 

0.97 
0.96 

0.93 


0.87 


118.74 
119-58  °;g4 
120.41 

121  21 

'  3  0.81 

123-63  °'!9 


*» 

125.96  °-77 

i26.?3  :^s 

-748    ' 


131.86 

132.57  °'!0 
133.27  •' 

133-97   'go 
134.66  o'J^ 

'35.34  0;68 


0.66 

-       0.65 
139-99  °  Is. 

5E3  3 


143.16 


146.23 
146.83 
147-43 
148.03 


"J 


3 

0.6o 


103.04 
104.08 
105.10 
106.1 1 
107.11 

108.10 
109.07 

IIO.O2 
110.97 
111.90 

112.82 


A 
1.04 

1. 01 
1. 00 
0.99 

0.95 
0.95 
0.93 
0.92 


117.26 

Ii8.ii  °-8s 
118.96  °'8s 
119-79  ° 


123.0 


0.78 


126.91    °'7° 
127.66    °'7S 

I28.4I    °'7S 
0.73 
129.14 

129.87   "'I3. 


132.02 

132.72 
133-42 
I34.II 

134-79 
135-47 


0.70 

0.70 
0.69 
0.68 
0.68 
0.67 


j   0.65 
0.65 

IB? 

£83 

I42.6O 

Q-»     O.6l 

I43'"3      f. 

•    /I        *     O.OI 


°-s9 


146.85  ° 
147.44 

148.62 


105-31 
106.32 

107.32 
108.31 

109.28 
110.24 
111.19 

112. 12 
II3.04 


°'9S 


0.91 


II748 

118-33 
II9.I8 
I2O.OI 


124.04 

I24\82 

-5-59 


°-80 

°-79 

°'78 


127.10 


0.75 
° 

°'7S 


129.32 


130.77    °'7 
131.48 
132.18    °'70 

132.88    °'70 
0.69 

133-57    0 

Hi 


• 


139-53 

I40.J7 
140.80 

I4I-43 


143.28 
I43-89 


0.61 
o.6r 


I45-69 
146.28 
146.87 


148.62 
149.19 


ii 


110.46 
111.41 
112.35 


116.84  °- 


119.40 
120.23 
121.06 
121.87 
122.67 

123.46 
124.25 
125.02 


0.80 
0.79 

0.79 
0.77 


127.30 
128.05  °'7S 
128.78  °'73 

O  73 
129.51          'J 

I30.23    °  7,. 

130.94  0 

III 

'34-41 
135-08  °-°l 


140.90 


146.90 

H7.48 
148.06  °'s8 
4s.63  "  " 
149.20 

149.76 


°-57 
°-57 

0.56 


°-9S 
°-94 


0.06 


111.64 
112.58  °'94 
II3-50  ° 
114.41 

"5-3'  0^89 
116.20 

117.08  °-88 

"7-94  :  ' 

"8-79  "I! 
119.63  o'g* 

120.46 
121.28  ° 

'22.09  °'a' 

122.89 

123.68 

124.47 
125.24 
I26.0O 
126.76 


"S3 

-9-70 
130.42 


138-49 


\j  s  i 

140.38 
141.00 

141.62 


0.62 
0.62 

0.61 
0.60 
0.60 


144.62 


0.79 
0.79 

0.77 


150.33 


107.97 
108.97 
109-95 
116.92 


113.74 
114.65 


"9.87 
120.69 

* 


123.91 
"4  69 


126.97 
127.72 
128.45 

129.18 


3 


0.82 


/y 


0.73 

0.72 
0.71 


134-74 
I35-40 

136.06 
136.71 
137-35 
137-99 
138.63 

139.26 
139.88 


0.60 


141.72 

142.32 
142.92  ° 

'£» ° 
144.69 


145.28 
145.85 

147-56 

148.12 
148.68 
149.24 


0.59 


0.5 


150.8 


109.20 
110.18 
in.i6 

112. II 
"3-05 

113.98 
114.89 


„ 

°'98 
°'98 


"7-56 


120.11 


:•  2 

°4 

3 


122.56 
123-35 

124.92 
125.69 

126.44 
127.19 

127.93  ;•;; 
128.66  °-73 

129-39  °'!3 


0.78 
0.77 
0.75 

0.75 


133.57 
134-24 
134-91 
135-57 
136.22 

136.87 
137-51 


0.67 
0.6 


139-39 
140.01 
140.63 


143-03 
143.61 
144.20 
144.78 
145-35 

145-92 
146.49 


0.64 

0.63 
0.62 
0.62 

>.62 

).6o 


0  ,8 
0'58 
°'59 
-« 


a 


149  27  °-SS 
149.81  °'54 

150.35  ° 
150.89  °'S4 

*  0.54 
151.43 


60 
61 
62 
63 
64 

65 
66 
67 
68 
69 

70 
71 
72 
73 
74 

75 
76 
77 
78 
79 

80 
81 
82 
83 
84 

85 
86 
87 
88 
89 

90 
91 
92 
93 
94 

95 

96 
97 
98 
99 

100 
101 
102 
103 
104 

105 
106 
107 
108 
109 

110 
111 
112 
113 
114 

115 
116 
117 
118 
119 

120 


TABLES    FOR    THE    TRUE    ANOMALY. 


21 


M 


=  .36 


<  =  -37 


.38 


«  =  -39 


e  =  .40 


e  =  .41 


e  =  42 


M 


148.03 

;  148.62 

!  I49-2I 

!  149-80 

I  150.38 


I5I-54 
152.11 


152.68  °-57 
'53-25  ° 


155.50  -~ 
156.05  ^2 

156.61 
I57-I6  °-ss 
I57.7I  ° 

!S:S  - 

0.54 
159-34  „  ., 

159-88  °'*4 

160.42 

160.96 


120 
121 
122 
123 
124 

125 
126 
127 
128 
129 

130 
131 
132 
133 
134 

135 
136 
137 
138 
139 

140 
141 
142 
143 
144 

145 
146 
147 
148 
149 

150 
151 
152 
153 
154 

155 
156 
157 
158 
159 

160 
161 
162 
163 
164 

165 
166 
167 
168 
169 

170 
171 
172 
173 
174 

175 
176 
177 
178 

179  179-56 

180  180.00 


0.58 
0.57 


0.54 
0.53 
0.53 


162.02 
162.56  °'54 
163.09  ° 
163.61   s 
164.14  °-53 

164.67 
165.19 
165.71 
166.23 
166.75 

167.27 

l67-79  ° 
168.31      5 
168.82  °'51 
169-34  °05sl 
169.85  n 


0.53 


0.52 


/   '^  0.51 

17241  0.SI 
172.92 

,„  ,,  0.51 

1/343  0.50 

•73-93  0  * 

•74-44  :;>5; 


176.47 

176.97  °-S° 
/   0.51 

177.48 
,77-98  °-50 
1/8.49  ° 


148.62     * 

'49-78  «•*« 
I50.35  „ 


g;49  O.s 

'52-62  °'l 


•53-74 


6 


155-40 
155.95 
156.50 


158.12 

158.65 


•59-72 
160.25  " 
160.78  °-s3 

161.31  °"S3 

161.83  °-52 

J  0.53 
162.36 
,62.88  °'S2 
163.40  ° 
,63.92  * 
,64.44 

164-95 
'65.47 
165.98 
166.49 
167.00 

167.51 

168.02  °-SI 

168.53  °'SI 

169.03  ° 

169-54  0;^0 
170.04 


0.51 

0.52 


0.51 


I72'55 
173.05 

'£5? 


0.50 
0.50 


$:£  - 

178.52  °o 
,79.0,  o'49 

180.00 


150-33 


ss 


154-23 

'54-77 
I55-32 
155-86 


.ss 


156.93 

157-47 
158.00 

158.53 
I59-05 
159-58 

160.10 

,60.62  °'52 

,61.14  °'52 

,61.66  °'S2 

,62.17  °'SI 
'  0.52 

162.69 

'63-26  °-f; 


~f      O  SO 

166.24 
,f*.  -7  °-s° 


167.74 
168.24  °-S° 
168.74 
169.24 


0.49 


172.20 
172.69 


174.16 

'74-65 


176.60 

'77-08 


'78-54  :•} 
179.03 


179-52 
180.00 


149.76 

150-33 
150.88 


153-09 


"54-17 
154-71 


o.ss 

0.54 
i.S4 


rs 

° 


156.84  °'S3 
157-36  ° 


0.52 
0.51 

'S^  °;ss* 
160.47 

'60-98  05, 
161.49  ° 
162.00 
162.51 

163.01 


0.51 
0.51 
0.50 


164.01 
l64-5' 


166.50  °'49 
166.99 

167.48  °'49 
0.49 

167.97 

168.46  49 

168.95  °'49 

ifinT.  °"*° 


°'49 

- 


170.41 
170.90 

•^•S 

171.86  °- 


172.83 
I73.3I 
173-79 
174-27 
174-75 

i75-23 
175-71 

176^66 

177-62 

1 78^57 


180.00 


150.88  " 
I5I-43  °-SS 
'Si-97  ° 


0.53 


153-05 
153-59 
154-12 

I54.65 
155-18 


157-27  :„ 

157-78  0;*2 

158.30 

158.81  °-SI 
159-32 
159-83 

160.33  _^ 

160.84 

161.34  ° 
161.84  °'s° 
162.34  °'so 

162.83 0-49 

°  0.50 


0.51 


0.49 
0.49 


164.31  °-49 

165.80  °'49 
'65-29 
165-78  _^ 

'<|w  *;« 

167.24 


167.72 


0.48 
0.48 

168.20 

168.68  °-48 

169.16  ° 

169.64 

170.12 


171.07 

172.02 
172.49 
172.96 


0.48 
0.47 

0.48 


°'47 

0.47 


0.47 


• 


O  47 

I77.I9 

0.47 

177.66 
I/8.I3  °'47 

178.66  °-47 
179.06  °'46 

179-53  °;47, 
180.00 


15088 


153-56 
154-08 
154.61 

155-65 
156.16 
156.68 
157-19 
157-70 
158.20 

158.71 
159.21 


0.53 


' 


0.51 

0.51 

0.50 
0.50 


160.70 


0.49 
0.50 

161.20 

161.69  °-49 

1 62. 18  °'49 
162.67  °'49 
I63-I6  "49 


163.64 
164.13 
164.61 

165.57 
166.05 


0.48 


167.00 

167.48 
167.95 


169.36 
169.83 
170.30 


0.47 
0.47 


178.62 
179.08 
179-54 
180.00 


152.49 
'53-01 
'53-53 


0.52 


52 


'54-57  . 
155-08  °'SI 

'55-59 
156.10 

156.61 

'57-" 

157.62 


0.51 
0.51 
0.51 

0.50 
0.51 


158.61 


0.49 
0.50 

I59-" 
159.60 
160.09  °'49 
160.58  ° 

161.55  0 
162.04 
162.52  °'4* 
163.00  °' 

l63-47  o^g 
163-95  „ 


165-37  l\H 
166.31  °'" 

168.64 
169.10  °'46 

ss  Hi 

170.49 
"  0.45 


'7-32 


,_^"    0.45 

O.46 

•75-4  :;:ss 

'75-49   6 
'75-95  „  4 
176.40  °'4S 
176.85  ° 
•77-30  °;« 

'77-75  0  ., 
178.20  °'4S 

178.65  °'4S 
179.10  °'4S 

179-55  °;4j 
180.00 


120 
121 
122 
123 
124 

125 
126 
127 
128 
129 

130 
131 
132 
133 
134 

135 
136 
137 
138 
139 

140 
141 
142 
143 
144 

145 
146 
147 
148 
149 

150 
151 
152 
153 
154 

155 
156 
157 
158 
159 

160 
161 
162 
163 
164 

165 
166 
167 
168 
169 

170 
171 
172 
173 
174 

175 
176 
177 
178 
179 

180 


22 


TABLES    FOR    THE    TRUE    ANOMALY. 


M 


-43 


.44 


-45 


.46 


.47 


.48 


-49 


M 


0 

1 

2 
3 

4 

5 
6 
7 
8 
9 

10 
11 
12 
13 
14 

15 

16 
17 
18 
19 

20 
21 
22 
23 
24 

25 
26 
27 
28 
29 

30 
31 
32 
33 
34 

35 
36 
37 
38 
39 

40 
41 
42 
43 
44 

45 
46 
47 
48 
49 

50 
51 
52 
53 
54 

55 
56 
57 
58 
59 

60 


o.oo 

2.78 

5-55 

8.32 

11.07 

13-81 

19.23 
21.91 


A 

2.78 
2.77 

2.75 

2.74 


••  • 


32.29  2'" 
34.80 

37-26  2'46 
2.43 

39-69  -  ,0 
42.08 

44-42  2'34 


55.48 
57.56 
59-60 

61.59 


67.32 
69.15 

70-93 
72.68 


1.83 
1.78 

1.75 


82.40 
83.90 
85.38 

86.81 
88.22 

89.61 
90.96 

92.28 

93.58 

94.86 
96.11 


1.48 
1.43 

1.39 
1. 35 

1.30 

1.28 
1.25 

1.22 


. 

8  -53 


«« 


102.01 


™  I.O? 

105.30  „, 

106.36  '-06 

IO7.4O  *"°4 

108.42  J-°2 

109-43  o'°g 
110.42 


o.oo 
2.86 
5-72 
8..S7 


si 
ss 


2'86 
2'8s 

a 


2.77 
2.75 

2.71 
2.68 

2.6S 


3576 
38.28 

40.76 
43-19 

45-57 
50.20 

52.45 
54-65 
56.80 

58.90 


62.97 
64.94 
66.86 

68.74 

70-57 


2.34 

2.29 
2.25 

2.IS 


- 


75.83     I'll 


80.75 
82.31 
83.84 
85-34 

86.81 

88.24 
89.64 
91.02 
92-36 
93-68 

94-97 
96.24 

9748 
98.69 
99.88 

101.05 

102.20 


1.56 
1.53 

1.47 
1-43 


.29 

•27 


1. 17 

I. IS 


104.43 
105.51 
106.58 

107'63  [H 

108.66  I>03 

109.67  I'°I 

110.66  °-" 
0.98 

111.64 


0.00 

2.95 
5.90 
8.83 

n-75 


2.93 
2.91 

2.88 


23.22 
26.01 

28.76 
31-47 
34-13 
36.75 

39-33 
41.86 
44-34 


53-75 

SS 

60.27 


68.29 


2. 75 

2.71 
2.66 

2.62 


73-82 
75-58 
77.29 

78.97 

82.21 
83.77 
85-30 
86-79 
88.25 


.48 


• 


• 


71 


91.07 
93-77 

96.36 

97.61 

98.84 

100.05 


102.39 
103-52 
104.64 

105-73 
106.80 

107.85 
108.89 
109.90 


o.oo 

3.04 

6.08 
9.11 

12.12 

IS-" 
1 8.08 
21.02 
23.92 
26.78 

29.60 


A 

3.04 
3.04 
3.03 

3.01 

2.99 

2.97 
2.94 


43-00 
50.41 

55-08 
57-33 


2.S2 


63-77  £ 
65.81 
67-80  '•' 


73-49 


7878  '•? 


82-°8  E 
83.68 

85.24  • 
86.76  ;•» 

88.25  !-4 
89.70 


9-50 


112.85 


95.19 
96.49 

97.76 
99.00 

IOO.22 


10372 
104.84 

105-95 
107.03 
I08.O9 

109.13 
110.15 

IU.I5 
112.13 

114.05 


1.42 


- 


1.27 


1. 12 
I. II 
1. 08 

1.06 
1.04 

1. 02 


O.O7 


O.OO 

6^28 
9.40 


21.66  3'02 
24.64  2'98 


36:?2  2-8° 

38.86  2'74 

2   6O 

41-55  36l 
44-I7  .,.„ 

11  s 
is  s 

63!?! 2-17 
65.22 2-i1 

0  2. OS 


71.23 

73-4 

74-99 


83.58 

85.17 
86.72 
88.24 

8971 
9I.I6 


1.47 
1-45 
1.41 


I.I 

93-94  ,  ' 
95-29  . 
96.61     ' 

97-89 1;] 

99-15  - 

100.38 

101.59 

102.77 

103.92 

105.06 
106.17 


1. 21 

1.18 


1.14 


110.39 

!  1  1.40 


o.oo 

6^8 

9.70 

12.91 

1 6.08 


3'22 

3'21 
3-17 


39-97 

45-39 
48.01 

50-56 
53-05 
55-48 


62.39 
64.58 
66.70 

68.77 
70.78 

72.74 


78.31 
80.07 
81.79 


86.67 
88.21 
89.72 
91.19 
92.62 

94.02 
95-39 
96.73 
98.03 

99-30 

100.55 
101.77 
102.96 
104.13 
105.27 

106.39 
107.49 
108.56 
109.61 

1 1 1. 66 


2 


I>S4 


1.47 

:-43 


1.03 

1.02 
0.99 


O.OO 
6^69 


3'33 


13-33 
1 6.60 


2.99 


"-•»  2.7 

43-92  2;7 
46.65  , 


54-43 
56.89 

59-29 
61.62 
63.88 
66.08 
68.22 

70.30 


s 


2. 2O 
2.14 
2.08 

.02 


-62 

.55 


39 


115-25 


116.45 


83-32 
84.98 
86.60 

88.18 
89.72 
91.22 
92.68 
94.10 

95-49 
96.84 
98.16 
99.46 
100.72 

101.95 
103.16 
104.34 

105-49 
106.62 

107.72 
108.80 
109.86 
110.90 
111.92 

112.92 
113.90 
114.86 
115.80  °'94 

116.72  °'92 
0.91 

117.63 


21 

18 

IS 
13 
IO 


-02 

.00 


°-98 


0 
1 
2 
3 

4 

5 
6 
7 
8 
9 

10 
11 
12 
13 
14 

15 
16 
17 
18 
19 

20 
21 
22 
23 
24 

25 
26 
27 
28 
29 

30 
31 
32 
33 
34 

35 
36 
37 
38 
39 

40 
41 
42 
43 
44 

45 
46 
47 
48 
49 

50 
51 
52 
53 
54 

55 
56 
57 
58 
59 

60 


TABLES    FOR    THE    TRUE    ANOMALY. 


M 


-43 


-44 


«  =  -45 


.46 


-47 


e  =  .49 


if 


60 
61 
62 
63 
64 

65 
66 
67 
68 
69 

70 
71 
72 
73 
74 

75 
76 
77 
78 
79 

80 
81 
82 
83 
84 

85 
86 

87 
88 
89 

90 
91 
92 
93 
94 

95 
96 
97 
98 
99 

100 
101 
102 
103 
104 

105 
106 
107 
108 
109 

110 
111 
112 
113 
114 

115 
116 
117 
118 
119 

120 


110.42 
'"•39 


114:22  °'93 
0.92 

115.14 
116.04  °-9° 

"6'93  o"8,?. 
117.80  °'87 

118.66  °'8t 
0.86 


0.79 


134-43  - 
135.09  •• 
135.74  ••' 

'36'39  *6 
137.03  °' 


138.92 
'39-54 

140.76 
141.36 
141.96 

H2.55 
I43-I4 

I43-72 


145-44  "•" 

'46-°°  ::S6 

146.56 
147.12 
147.67 


151-44 
151.96 


"'•64  t, 

112.65  0'96 


114.47 


121.18 
1 22.00 
122.80 

123.59  0  79 

125  IS   °'77 

125.92  °"77 
126.67  °'7S 

0.75 
127.42 

128.76  °'74 

128.88  °-72 

129.60  °-72 

0.72 
0.70 

131.02 


-* 


°-60 


0.58 
0.58 


°'s6 
"•" 


148.22  °-ss 
148.77  °'ss 

0.54 

1M.&S   °'S4 
'•S3 


116.29 
117.18  °'*9 

118.06  °'88 

118.92 

"9-77 

120.60 

0.83 

122  2 S  °'82 
123^5  °-8° 
123.84  °'^9 

124.62 

:s  °- 
126.91  °-7s 

"7-65  ^ 

128.38 
129.11 
129.83 

130.54 
131.24 


I37.84 

138-46 
139.08 


0.63 

0.62 


0.73 


147.20 

T  JT  T  J   °*54 

I47-74  .  .. 
148.28  °'54 
148.82  °'S4 
H9-36-4 


152.50 


II2?85     A 
"3-80  °-9S 

"4'73  0^2 

"*3  :i 


120.03 

120.86 


0.83 


:s5  "> 
%s  3 

128.62  °-73 
0.72 

I29'34  0.7I 

0.71 
0.70 
0.68 


0.68 
0  66 


'35-47  o;oj 

'36-12  0.63 
!^'75  0.64 


'43-95  ;;„ 

'45-°8  O.ss 
'45-63  IS 
146.19  „ 


IS'S  °-s3 

I48;??  o.l43 


s, 

o 


150.46 
150.98 

152.01 
153-02 


"7-70  i;i 

118.58 

"9-44  0;a 
120.29 


122.76 


75 


126'65 
127.40 

128.13  °'73 

128.86  °'73 


si 


135.03 
135.67 
136.31 

136.95 
137.57 
138.19 
138.81 
139.41 

140.02 
140.61 
141.20 


" 


r 


°-59 


I42'94  0.57 
\A4-64  °-s6 

^•'94  :- 

ISS  -» 

146.83 
147.37 
147.90 

148.43 
148.96 
149.48 

150.00 
150.52 

151-03 


°'S4 


0.53 


°'S2 


o.so 


153.54 


117.08 
••»*» 


«• 

-•• 


"303 


'33-27  0.67 
'33-94  0.675 

m 


'39-59  0.6o 
'4°-'9  0.59 


150.07 


S4 
'46'94  o  53 

147.47  ° 
148.00  °-53 

° 


:; 

o.so 


154-05 


isl  5 

"*» ::!! 

~.'fi  0.83 


0.79 


124.89 
125.66 


128.65 


°'76 


0.72 


130.78  "•" 
131.48  0-7g 

11 


146.37  °-59 

'4°-*  :n 


142.68 


'44-36 
144-90 
'45-45 
'45-99 


148.10 
148.62 
149.13 
149.64 


°-s7 


* 


« 

« 


152.14 

152-6] 


154.08 
154-55 


"3- 


0.86 

121.12   °'8S 
0.83 

121.95  0 

HI 


-  0.76 

I26'7°  o  74 

127.44 

I28.il  °'74 


131-73 

'32-4'  IT7 

'33-08  0.67 
133-75  I II 

1  "U..J.O 
*^          0.6S 

'35-05  0.6> 
'35-69  0.6^ 

'36-32  0-63 
'36-95  0.6, 

1512  °-6' 

138.78 
'39-38  o_sQ 


141-14  O'll 

141-72  0;*7 

142.29 

,  Sc  °'S6 


S4 


145.05 

'45-59  0 
146.12  °'S3 

146.65  °'53 

147.18  °'S3 
0.52 

147.70 

148.21  °-SI 

148.72  °'SI 

I49-23 

149-74 

150.24 

150.73 

151-23 

151.72 


152.20 


0.50 

0.49 
0.50 

0.48 
0.48 


0.47 


I54-H 
154-58 

155-05 


60 
61 
62 
63 
64 

65 
66 
67 
68 
69 

70 
71 
72 
73 
74 

75 
76 
77 
78 
79 

80 
81 
82 
83 
84 

85 
86 
87 
88 
89 

90 
91 
92 
93 
94 

95 
96 
97 
98 
99 

100 
101 
102 
103 
104 

105 
106 
107 
108 
109 

110 
111 
112 
113 
114 

115 
116 
117 
118 
119 

120 


24 


TABLES    FOR    THE    TRUE    ANOMALY. 


M 


-43 


«  =  -44 


-45 


.46 


=  -47 


e  =  .48 


e  =  .49 


If 


120 
121 
122 
123 

124 

125 
126 
127 
128 
129 

130 
131 
132 
133 
134 

135 
136 
137 
138 
139 

140 
141 
142 
143 
144 

145 
146 
147 
148 
149 

150 
151 
152 
153 
154 

155 
156 
157 
158 
159 

160 
161 
162 
163 
164 

165 
166 
167 
168 
169 

170 
171 
172 
173 
174 

175 
176 
177 
178 
179 

180 


152-49 

153-52 
154-03 

154-54 
155-05 
155-55 
156.06 

156-56 


o.si 

0.52 


'SI 


0.50 


0.49 

0.49 
'0°-OJ  o  40 
159.02 

0.49 

'59-51 

159-99  ° 

'60-47  HI 


16218  °'48 

162^5  °'47 
163.32  HI 

163-79  0;47, 
164.26 

'65-19  °'4I 


0.46 


0.45 
0.46 

0.45 


I66.I  I 

166.57 
167.03 

167.95 
168.40 

168.86 
169.31 
169.76 
170.22 
170.67 

171.12 

I7I-57 
172.01 


'73-36 

'73-80  HI 
174.25 
174.69  °'44 

S3  rj 

175.58 
176.02 

0.44 


0.44 


176.91 
177-35 

177-79 

178^68 
179-12 
I79-56 

iSo.OO 


152.50 
153-01 
153.52 
154-02 
154-53 

I55.03 
155-53 
156.02 

156.51 
157-00 

157-49  o 
I57-98  -2 
158.46 

158-94  o 

159-42  0;47 

159.89  0 
160.37  4 
160.84  °'47 


0.50 
0.50 

0.49 
0.49 
0.49 
0.49 


161.78 

162.25 
162.71 
163.18 
163.64 
164.10 

164.56 
165.02 


0.47 


0.46 


166.38  ° 

0  0.45 
166.83 
167.28 

\68'7i8  °'4S 

168.63  °'4S 

0  0.44 


0.45 

t%.g6  °'44 
170.40  °' 
170.85   ° 

171.29 


0.44 


0.44 


I7L73 

172.61 
173.04 

17348 
I73-92 
I74.36 
174-79 

175-66 
176.10 


'6-97  n4 

'77-40  HI 


178.70 
I79-I3 
179-57 


0.44 


153-52 
154-02 
I54-52 
155-01 

I55-50 
155-99 
156.48 
156.96 
157-44 


A 

0.50 
0.50 


0.47 
0.46 


158-87 

159-34 
159.81 

160.28 
160.74 
161.21 
161.67 
162.13 

162.59 
163.04 


163.95  °'4S 

164.46  °-45 

0.45 

as  -« 

!S£  -« 

166.64  °'4.4. 
167.08 


0.44 


0.44 


0.43 


0.43 


180.00 


0.43 


167.96 
168.40  °-44 
i68.84  °-4? 

169.28 
169.72 
170.15 

170.59 
171.02 

\l\il  M4 

172.32  ° 

172.75  °'43 

J73-18  HI 

174.04  °'43 
174.46 
174-89  0 

175-32  in 

175-75   o 

176.17    '*; 
176.60 
177.02  ° 
'77-45  044l 
177.88 
178.30    ' 
178-73  o 

179-15    ' 
179.58     43 
0.42 

180.00 


153.54 
154-03 
154.52 
155-01 
155.49 

155.97 
156.45 


157.40 
157.88 

158.34 
158.81 
159.28 
159-74 

160.20 


0.46 


160.66 
l6l.II 

!S:S  -« 
162.47 

162.92 


.46 


0.45 
0.45 


163.82  4s 
164.26  °-44 
164.70  °-44 

165.14 


0.44 


166.02 
166.46  °-44 
166.90  °-44 

167-33 

Ibl'.lo  °'44 
168.63 


0.43 


0.43 


169-49 


170.34 
170.77 
171.19 

171.62 

172.04 


173-31 
173-73 


0.43 


0.42 

0.42 

0.42 
0.42 


175-83 
176.25 
176.66 

177-50 
177.92 
178.33 
178.75 
179.17 

179-58 

180.00 


0.42 


0.42 


156.91 


0.48 
0.48 
0.48 

0.47 

0.47 
0.47 
0.46 


160.58 

161.03 
161.48 
161.93 
162.37 
I62.8I 

163-25 


°-4S 

0.4S 


0.44 


164.57 
165.00 


°-44 
°-44 


0.43 


illsl  °-43 
166.29  °-43 
166.72  °-43 
167.15  °-43 

'   J  0.43 
167.58 

168.00  °'42 

168.43  °'43 

168.85  °-42 
169.27  °-42 

'  0.42 
169.69 

170.11  °'42 
170.53  °'42 

'70-95  n'4T 
171.36 

171.78 
172.20  °'42 

A  *  T 
I72.6I 

I73.03 
173-44 

173.85 
174.26 


0.42 


' 


O.4I 


I75-09 
175-50 

175.91 
176.32 

176.73 
177.14 

177-55 
177.96 

178.37 
178.77 
179.18 
179-59 
iSO.OO 


154-55 


A 

0.48 
0.47 


156.90 
157.36  Hi 
157.82  °'46 
158-27  II5, 
158-73  "Is 
159.18 

I59-63  „ 
160.07 
160.52  °'4S 

I60.96  °'44 
0-44 
161.40 
161.84  °'44 
162.28  °'44 
162.71  °'43 


164.44 
164.87 
165.29 

165.72 


0.43 


0.41 


' 


166.56 

167.40 

167.82 
168.24 
168.65 
169.07 
169.48 

169.89 
170.30 
170.71 
171.12 

171.94 


173.16   °'4° 

'73-57  o^ 

'73-97  ... 
'74-38  °'4' 
174.78 
175-18  °'4° 
'75-59  olo 
175-99 


177.60 

178.00 
178.40 
178.80 
179.20 
179.60 

180.00 


0.40 
0.40 


0.40 


0.40 


0.47 
0.46 


157-35  „  .. 
157.80  °-4S 
158.25  °-45 
158.70  °-4S 
'59-H  0- 


160.46  u 
160.90  °'44 

161.77 
162.20  ° 
162.63  °'43 

163.48  °'43 
0.42 

163.90 

1*5  in 

lAr    lA    O.42 


0.42 


0.41 


0.40 


166.00 
I66.4I 
166.83 

167.65 

168.06 
168.47  °'41 
I68.87  °-4° 

169.28  °-4! 
169.69 

170.09 
170.49 
170.90 
171.30 


172.10 
172.50  "• 

173-30  °'4° 

'73-69  o^o 
174.09 

174-49  °'4° 

174.88  39 

175.28  °-4° 

'75-67  0;39, 
176.07 

176.46  °'39 

176.86  0'4° 

I77-25  " 
177.64 


178.04 

178-43 
178.82 
179.21 
179.61 

180.00 


0.40 


0.39 


120 
121 
122 
123 
124 

125 
126 
127 
128 
129 

130 
131 
132 
133 
134 

135 
136 
137 
138 
139 

140 
141 
142 
143 
144 

145 
146 
147 
148 
149 

150 
151 
152 
153 
154 

155 
156 
157 
158 
159 

160 
161 
162 
163 
164 

165 
166 
167 
168 
169 

170 
171 
172 
173 
174 

175 
176 
177 
178 
179 

180 


TABLES    FOR    THE    TRUE    ANOMALY. 


M 


e  =  .50 


e  =  .51 


.52 


-53 


=  -54 


«  =  -55 


.V 


0 

1 

2 
3 
4 

5 
6 
7 
8 
9 

10 
11 
12 
13 
14 

15 

16 
17 
18 
19 

20 
21 
22 
23 
24 

25 

26 
27 
28 
29 

30 
31 
32 
33 
34 

35 
36 
37 
38 
39 

40 
41 
42 
43 
44 

45 
46 
47 
48 
49 

50 
51 
52 
53 
54 

55 
56 
57 
58 
59 

60 


0.00 


10.35 
13-77 

20-49 
27-03 

30.22 

33-34 
36-40 


45-^7 


3-38 


3-12 


2.09 


a  s 
ss  ^2 

60.76 
63.11 2-3f 
65.39 2 

67-61  !•!! 
69.76 

71-85 
73-87 

77-75 
79.61 

81.41 
83.16 

86^53 
88.14 

89.71 

92.72 
94-17 
95.58 

96.96 

98.30 

99-61 
100.89 
102.13 

103-35 
104-54 
105.71 
106.85 
107.96 

109.05 

IIO.I2 
III.I6 
112.18 

"3-19    - 

"til   0.96 


°-93 

°'91 
0.90 


•  7S 
-71 

.61 

•  57 

•  52 


•  41 

•  38 


•  4 


.07 


117.01 
117.92 

II8.82 


0.00 

3-58  "« 

7-15  ** 

10.70  J 

14.23  3"S3 

h     °  3-49 
17.72 

21.16  3'44 


27.90 
31.17 

34-38 


49-3° 


3-27 
3-31 

3.14 
3-06 
2.98 


2  7S 


62.28 


2-37 


71'33  2'op 

8S  S 
S3  *" 

81.19 
82.99 


88.08 
89.68 

91.24 
92.76 
94-23 
95-67 

98.43 

9976 

101.05 

102.32 

103-55 

104-75 
105.93 
107.08 
108.20 


110.37 
111.42 

112.45 


M 

Ml 

•7S 
.69 


•  29 

•  27 


.18 

•  IS 

.12 
.IO 


119.99 


0.00 


A 
3-71 


28.81 
32.17 

35.46 
38.67 


£5 

56.20 


3-36 
3-29 

3.21 
3-05 

2.87 
2.80 


as 

68.53 


75-03 
77.06 

79-03 
80.94 

84.58 
86.32 

88.01 


91.24 

92.79 
94.29 

95-75 


99.90 

IOI.22 
102.50 

103-75 
104.96 

106.15 
107.31 
108.45 
109-55 


II2-73 
"3-74 
114.74 


2.03 

-97 
•91 


.55 


•  32 
.28 
.25 

.19 


II6'66 

!£?? 


0.95 
0.93 


o.oo 


ii.46  3-8° 

'5-3 


26.22    3'6° 

29-75  *» 
33-21 


43-08  3'20 

46.19 

49.21 


3'02 
2.92 


70.15 


2-33 


2.03 


76.66 
78.69 

80.66  I'97 

82.56  l'jj° 

86.19  ' 

87-92  ''73 

89.60  j-°8 

92.81  I-s8 

1-53 

94-34  , 


97.28 

98.68 

100.05 

101.38 
102.68 

103-95 
105.18 
106.38 

107-55 
108.69 

110.90 


1.37 

1-33 

1.27 

1. 20 
t.I7 

1.14 


116.96   °'96 
0.94 
117.90 

118.82    °-92 
¥lr.  _,    0.90 


121.16 


121.47 
122.32 


2     A 

54-97    '  < 


o.8s 


O.OO 

3'97    I'll 
7-94   3 

15-77 
19.62 

27.12    3'72 

34-30  3;^ 

4"3  3 

KS  HI 
50.65 


53-62 


2.97 

2.87 
2.78 


67.05 
69.46 
71-79 
74-05 
76.22 

78.32 

80.35 
82.31 
84.21 
86.04 

87.82 


2.41 
2.33 
2.26 
2.17 
2.  IO 

2.03 


1.78 


92.82 
94-38 

95-90 

97-37 
98.81 
1 00.20 
101-55 
102.87 
104.15 

105-39 
106.61 
107.79 

108.95 
110.07 
111.17 
112.25 
II3-30 


1.28 


1'°" 


o  88 


o.oo 

4'12  i" 

8  4-  * 1 
.2* 

12.30  4-07 

16.34  4'04 

°*  3.97 

20.31 

24'22  I'll 
28.05 

31.80  3 

35-45  t 


'  4 


42-44 

45-78 

49-01 


63-58 
66.20 

68.71 

73^8 
75-73 
77-91 
80.00 
82.03 
83.98 
85-87 
87-69 
89.46 
91.16 
92.82 
94.41 
95-96 

97-47 

98.92 

100.34 

101.72 

103.05 

104-35 
105.61 
106.84 
108.04 
109.20 

110.34 

112.53 

"3-59 
114.62 


2.SI 


2.09 


77 

-n 

t.', 

H 

55 
ft 

45 
-? 

33 
30 


^3 

1 6 
1.14 

I. II 
1. 08 
1. 06 
I.O3 
I.OI 

0.96 


123-47 


120.35 

121.24 
122.96 

123.79 

124.61 


0.89 


O.OO 
4.28 

8-54 

16.94 

21.05 

25-09 
29.04 
32.89 


4.28 
4.26 


4.11 


40.28 

43-80  I'll 

47.21  3  4 

5°-50  33H 

53-68  g 


75-19  :  ,6 

77-45  ai7 

2.09 
81.71 
83-73  2'°2 
85-67 
87-55 


92.80 

94-44 
96.02 

97-55 

99.04 

100.48 

101.88 


103-23 

105.83 
107.08 
108.29 
109.47 
110.62 

1 1 1-73 
112.83 
113.89 
"4-93 
"5-94 


.49 


•32 
.28 


-5 


.II 
.10 


118.85  °'9S 
119.78  °'93 

120.68  °-9° 
0.89 

l^-s?  0.87 

,,'in  °-85 


125-75 


0 

1 

2 
3 

4 

5 
6 
7 
8 
9 

10 
11 
12 
13 
14 

15 
16 
17 
18 
19 

20 
21 
22 
23 
24 

25 

26 
27 
28 
29 

30 
31 
32 
33 
34 

35 
36 
37 
38 
39 

40 
41 
42 
43 
44 

45 
46 
47 
48 
49 

50 
51 
52 
53 
54 

55 
56 
57 
58 
59 

60 


26 


TABLES    FOR    THE    TRUE    ANOMALY. 


M 


.50 


.51 


.52 


e  =  -53 


-54 


e  =  -55 


-56 


If 


60 
61 
62 
63 
64 

65 
66 
67 
68 
69 

70 
71 
72 
73 
74 

75 
76 
77 
78 
79 

80 
81 
82 
83 
84 

85 
86 
87 
88 
89 

90 
91 
92 
93 
94 

95 
96 
97 
98 
99 

100 
101 
102 
103 
104 

105 
106 
107 
108 
109 

110 
111 
112 
113 
114 

115 
116 
117 
118 
119 

120 


n88a 


"isf  °-81 

^V'  0.80 

I25;45  °'I! 
126.22 

0.76 

126.98 
127.72  °"74 
128.46  °'74 
129.18  °'72 
129.90  l^ 


J  0.66 

'33-99  „  „ 


'35-93  H4 
'36-55  °066l 

Si::" 

139.00  °- 

139-59  O'll 
140.18 

140.76  °-s8 

i  11  °-57 


142.47 

I43-03 
I43-58 
I44-I3 
144.67 
145-20 

145-74 
146.26 
146.79 


0.55 
0.55 
0.54 

0.54 
0.53 


,   .  _  o  —    uoi 

147-82 

0.51 

148-33   „  „ 
148.84  °'SI 


150.33 
150.82 


0   SO 

°-so 


iis'3 

155-54 


;22;54  ZZ 

0.8 1 

124.17 

I2F4  °:77 
126.51 

127.26  °-7s 
0.75 
128.01 
128.74 
129.46 
130.18 
130.88 


" 


'3'  -57 


0.69 


'34-90  0  6 


'37-41 


143.76 


145.37 
145.89 
146.41 


54 


147.95 
148.46 

149.45 
149.95 


0  „ 

„ 
°-SI 

0.50 


'5°-92 


151-88 


'53-29 


' 


0.47 
0.47 


155.13 

155.58 

156.03 


\\iil  ^ 

126.87  °'77 
127.56  °'7S 


II 


'37-04 


'39-44 


140.61 
'4"'8 


0.59 
0.59 

0.59 
0.58 


14340 
143-94 
144.48 
145-01 

145-54 
146.06 

H6.57 

147-59 
I48.IO 
148.60 
149.09 

149.58 
150.07 
150.55 
I5I-03 


o.so 
° 

°'SI 
°-so 


153-82 
154.28 
154-73 
155-18 
I55-63 
156.07 

156.51 


0.47 
0.46 
0.45 
0.46 

0.45 


°'44 
0.44 


I2232 


127.86  °'7S 
128.60  0'74 

129-33  °;" 

130.05 
130.76  °-?' 


'33-48 


0.67 
0.66 


0.62 


139-68 
140.26 

4o.83 


°-s8 

°'S7 


°'54 


I45.I9 

14572 
146.23 
146.74 
I47-25 

147-75 
148.25 
148.74 


0.51 
0.51 

0.50 
0.49 

0.49 


: 


•54.35 


I23-47 


1 26166  °'78 
0.76 

127.42 
I28.T7  °'7S 

128.91  °-74 

130.35  °;7i 

131.06 
,f .  _,  0.69 

0.68 

'33-77  0  05 

II 


138.76    ; 

139-35       ,g 

139-93  0;S7 
140.50  ' 
!4!-°Z  o.ll 


156.98 


143-27 
143.81 

144-34 

144.87 

145-90 
146.41 
146.92 
147.42 
147.91 


149.38 

IKS 

13    "** 


.. 

;  4 


0.51 

0.51 

0.51 


0.47 
0.47 


'5I-73 


0.45 


155-31 
155-75 
156.18 
156.60 
157-03 

157-45 


126.21  u 
126.98  °-77 
127.74  °-76 

*   0.75 
128.49 
129-23   °'74 


'3''37  o09 

II 


139-02  o 
'39-60  °-5l 
140.18  °'s8 
'40-75  -7 


142.42 
142.96 
I43-50 
144.03 
144-55 
I45-07 
145-59 

146.60 
147.10 
147.60 
148.09 

I49.05 
149-53 
150.00 

150-47 
150.94 


-* 

0.55 

"• 

-4 


°-s° 


„ 


153.65 

'54-09 


., 


!56.66 


157.91 


°'42 


18:3 


128.82 

129.55 
130.28 


7, 

; 


-• 


» 

SJi  « 

0.59 


142.11 
142.66  °of4 

'4373  °;" 


144-77 
145-29 
145.80 

146-30 
146.80 

I47-30 


0.51 
0.50 
0.50 
0.50 

0.49 
0.48 
0.48 


152.88 

I53-76 
154-20 
I54-63  . 
155-06  °'43 
15548 
155-90 

156-32 


o 


157.56 
157-97 

158.37 


: 

°4 


60 
61 
62 
63 
64 

65 
66 
67 
68 
69 

70 
71 
72 
73 
74 

75 

76 
77 
78 
79 

80 
81 
82 
83 
84 

85 
86 
87 
88 
89 

90 
91 
92 
93 
94 

95 
96 
97 
98 
99 

100 
101 
102 
103 
104 

105 
106 
107 
108 
109 

110 
111 
112 
113 
114 

115 
116 
117 
118 
119 

120 


TABLES    FOR    THE    TRUE    ANOMALY. 


M 


e  =  .50 


«-  -Si 


e  =  .52 


-53 


-  -54 


=  -55 


120 
121 
122 
123 

124 

125 
126 
127 
128 
129 

130 
131 
132 
133 
134 

135 
136 
137 
138 
139 

140 
141 
142 
143 
144 

145 
146 
147 
148 
149 

150 
151 
152 
153 
154 

155 
156 
157 
158 
159 

160 
161 
162 
163 
164 

165 
166 
167 
168 
169 

170 
171 
172 
173 
174 

175 
176 
177 
178 
179 

180 


.55-54 
156.00 

156-45 


157-35 
157-79 


0.45 


0.44 


0.44 
159-12  °'44 

159-55  0;43 

159-99  0 
,60.42  °-43 
,60.85  °'43 
,61.28  °-43 

,61.70  °-42 
0.43 

f.i'ce  0-42 


164.22 

165.05 


,66.27 

,66.68  °'41 
,67.09  °"41 
167-49  °'4° 
l67-89  ^ 
168.29  „ 


::;: 


171.08 


,72.26 
,72.65 


°-39 


<"39 
°'38 


'75-76 


I77-30 
,77.69 

,78.07 
,78.46 
,78.84 

1/9-23 
,79.61 

,80.00 


0.38 
0.39 
0.38 

0.38 

0.38 
0.39 


I56°3 
'56-48 


157.36    ' 
'57-80  -44 

,58.24 
,58.67  °'43 
159-10  °'43 
159-53  ° 
'59-96  Q;43 

160.39 
,60.8?  °'42 
,61.23  * 


,62.07 

162.48 
,62.90 


0.41 


,64.13  °'41 
*    •  0.40 

Ii 

,66.15 
0  0.40 


•» 


0.39 


,69.3, 

,70.09 

,70.48 
,70.87 
171-25 


°-38 
S  3 

'73-94  0.38 


'75-46 
'75-84 


'77-36 
'77-73 


0.38 
0.38 

0.38 
0.38 
0.37 
0.38 

0.38 


157.38  rs 

157-81  !'43. 

158.24 

,58.67 
,59.10 
159-52 
159-94 
,60.36 

,60.78 


0.43 
0.43 


0.42 


°'42 


0.40 


,6, .6, 
162.02 
162.43 

,62.83 
163.24 
163.64 
164-4  °-4° 

164-44  °'40 
*  0.40 

,64.84 

i6s-24  :i: 
165.64  ° 

.66.03  °-39. 
,66.42 

,66.82 
,67.2,  °"39 
,67.60  °-39 
,67.98  °-38 
,68.37  °-39 

*'    0.39 
,68.76 

169.14    °'3 


0.40 


169.91 
170.29 

,70.67 


I72.,8 


172.94 

'73-31 
'73-69 
174.06 


0.38 
0.38 


0.38 
0.38 


0.38 


180.00 


,74.44 
,74.8, 
175-18  °-J7 

175-55  : 
175-92  03l 
,76.30 
,76.67  °'37 
,77.04 

177-4. 
,77.78 

178.15 
178.52  °-37 
,78.89  °-37 
,79-26  °-37 
.79-63  0;3^ 
,80.00 


„  „ 
°'37 


°'37 

°'37 
°-37 
0.37 


,56.98  * 

'Si;  r3 

S6  - 

,59.10 
.59.52 

.59.93 
.60.35 


0.42 

.-n 


,61.17 
,61.57 
,61.98 
,62.38 
,62.78 

,63.18 
.63.58 

ss  - 

,64.76  °-39 

*  '       0.39 


0.40 
0.40 
0.40 

0.39 


168.61 


0.38 
0.38 
0.37 

'£74  3 
,70.1,  •" 

'70-48  ^37 

\\\2<x>  °'37 
I71'97  0'37 

.72.34  °;" 

,72.7, 

,73.08  °-37 
.73.45  * 


180.00 


S 


.57.45  0  .. 
157-87 1 

'58-29  0'*\ 
'58-70  -4 

i  '59-'2  0.41 

'59-53  0 

159-94  o 

1  ,60.34     4 

i  j6o.75  o;4Q 

i6i.55  0 
:  ,61.95 

.62.34  °'39 


163.52 

163.91  °-39 
164.30  °-39 


£8  ::i 

;ss  - 

•  0.38 

,67.08 


I66'97 


.65-45     -  ,o 

.65-83    ' 

l66'21  03& 
0.38 
0.37 

lel'.T^  °-38 

,68.09  °'37 
,68.46  °'37 
,68.84  o 

,69.2, 
,69.58   °'3J. 
,69.94  °'36 

0.17 

.70-3.  :37 

,70.68  37 
0.36 

,71.04  o 


172-13 
,72.50 

,72.86 
173-22 
173-58 


0 


0.37 
0.36 


175-37 
175-73 
,76.09 

176.45 
,76.80  - 

,77-16  °'36 

177-51 

177-87 

178.23 
,78.58 
,78.94 
179-29 
179-65 

,80.00 


157-91 

158.33 

159-14 
159-55 

.59-95 


,6,:(4  °-39 

,61.54  °-4° 

"  0.39 
,61.93 
,62.32 

,62.7,  ° 


-    0.38 
,64.24  * 

,64.62  °-3* 

,65.00  -38 


165-75    „  „ 
,66.12 
,66.50  0'38 
,66.87  °'3! 


170.51  "-J" 

'7°-87  °0\?6 

171-23  . 

171-58  " '" 

I7L94  ' 
,72.30 

172-65  °-3S 


173.01 
173-36 
173-71 


°-" 
3 


175-47  I"  „ 
175.82  ~* 
,76.17 

:?6:i7  o- 

177.22 

177.56 

177-91  ;;3j 
,78.26 
,78.6,  ° 
,78.96  °-3S 
.79.30  -34 
.79-65  °;3* 
,80.00 


°-3S 


isVis  °-4°  , 
159-57  - 

I59'97   ol    j 

%$  3 


,61.92    3" 

I  I62'3°  0 
,62.68  °'38 

I  ,63.06  °/38 
3"       0.37 


°-34 

«•« 


,79.66 
180.00 


£5  s 

165-31 


166.04  0  „ 
,66.4,  °-37 
,66.78  ^;37 

0.36 
0.36 


3 


,67.86 

,68.22 

,68.58 
,68.94 
,69.29  "0-** 

\%&  °- 

!S3?  °-* 
;7;-o6  0;3SS 

17,76  °'3S 
172.11  °-35 
,72.46  °-3s 

,72.80  °-34 

0.3S 

173.15  „  „ 
.73.50  °' 

I"-8;}  oil 


I75-56 

.75-9.  : 
,76.25  o"" 

176.59  . 
.76.93  °'34 
177-27 
,77.62 
,77-96  °-34 

0.34 
178.30 
,78.64   °' 

0-34 


0.34 


120 
121 
122 
123 
124 

125 
126 
127 
128 
129 

130 
131 
132 
133 
134 

135 
136 
137 
138 
139 

140 
141 
142 
143 
144 

145 
146 
147 
148 
149 

150 
151 
152 
153 
154 

155 

157 
158 
159 

160 
161 

163 
164 

166 
167 
168 
169 

170 
171 
172 
173 
174 

175 
176 
177 
178 
179 

180 


TABLES    FOR    THE    TRUE    ANOMALY. 


M 


e  =  -57 


=  -59 


e  =  .60 


e  =  .61 


.62 


.63 


A/ 


0 

1 

2 
3 
4 

5 
6 
7 
8 
9 

10 
11 
12 
13 
14 

15 
16 
17 
18 
19 

20 
21 
22 
23 
24 

25 
26 
27 
28 
29 

30 
31 
32 
33 
34 

35 
36 
37 
38 
39 

40 
41 
42 
43 
44 

45 
46 
47 
48 
49 

50 
51 
52 
53 
54 

55 
56 
57 
58 
59 

60 


o.oo 

4-44 
8.86 


A 

4-44 
4-42 


13-25  T£ 
'7-57  4;*6 

21.83  ,  „ 
26.00  4'17 
30.07 
34-04 


4'07 


41.61 

45'22  3  J 

48-7°  I'll 
52.05  J  3 

55-27  3-" 
58.38 


g 


66.97 
69.62 

72.16 
74.60 

76.94 
79.19 

83-44 
8545 
87-38 

91.04 

92-78 
94-45 
96-07 
97.64 

100.62 
102.04 
103.42 
104.76 
106.06 

107.32 
108.54 
109.73 
110.89 

II2.O2 

113.12 
114.19 
115.24 
II6.26 
117.26 

118.23 

I2O.II 
I2I.O2 
121.91 

122.78 


126.8 


2.54 

2.44 


74 
67 

57 

51 
•47 

,3» 

34 

,26 

22 

19 


•  07 
.05 
.02 

0.97 
0.95 


O.OO 
4.61 
9-21 

18.24 
22.65 


4.60 
4-55 
4.48 
4.41 

4.20 


50.24  £ 

56'92  l'.l 
60.06 


78.71 

80.96 

85.19 
87.19 

90.96 


97.71 

99.26 

100.75 

IO2.2O 
103.60 
104.96 
106.28 
107.56 

108.80 
IIO.OO 

111.17 
112.32 
113.43 


116.59 

117.59 
118.57 

119.52 


••« 


127.23 

128.00 


O.OO 

4.80 

9-57 


A 
4.80 

4-77 
4-73 


.  JC 

: 


36.50 
40.56 

44-47 
48.23 
51.84 
55-31 
58-63 

61.80 


3.91 


75-74 
78.18 
80.52 

82.75 
84.90 

86.96 

88.95 
90.85 

94-44 

9778 

99-36 

100.89 

103.79 
105.17 
106.51 
107.80 
109.06 

110.28 
111.47 
112.62 


,  , 
2'44 


2'23 


*•'* 


0.77 


'  0.94 
120.81 

124-34  °:ii 

126.80  °-  ° 

128.36  °'77 
0.76 

129.12 


O.OO 

5.00 
9.96 


A 
4.96 


'9-7^ 


33-51 

37-83 

41.99 

y 


4'47 


4.00 

3.84 
3.68 
3-51 
3.36 
3.21 
63-59  ,07 

66.66  3'07 
69-53  '9o 

72-37  'I: 


45-99 

ss 

ss 


80.02 
82.35 
84.58 


2.54 
2.44 


•76  !. 


97-84  z.c 


103.97 

105.38 
106.74 
108.05 
109.32 
110.56 

111.76 
112.92 
114.05 


117.26 
118.27 
119.26 
120.23 
121.17 

122.09 
I23!S6 

124.71 
125-55 


,  ,6 
1>31 

1.27 

' 

I>24 
i.  20 


IlOX 

"•" 

0.07 

0.9! 
0.92 


127.96 
128.73 

129.48 
130.22 


°-7s 

0.74 


o.oo 

5-21 

10.38 
15.48 

20.50 

25-40 


39-22 

43-49 

47.58 
51-50 


5.17 
5.10 
5.02 
4.90 

4.77 
4-44 


3'74 


62.20  3'4° 
3-24 

65-44  ,no 


79.46 
81.89 
84.21 
86.42 

88.54 


2.54 
2.32 

2.21 
2.03 


94.38 

96.17 

97-89 


102.67 


106.97 
IO8.3O 

109-59 
110.85 
II2.O6 

113.24 

114.38 

115-49 
116.56 
II7.6I 

118.63 


1-33 
1.29 
1.26 

I. 21 

1.18 

1.14 
i. ii 
1.07 

I. O2 


121.54 


I24-23 

I25'°9 
125-93 


0.84 


I29.IO 
129.86 
I3O.6O 

I3L32 


°'77 

°-76 

°-74 
0.72 


O.OO 

5-43 
10.82 
16.14 

26.43 

36.11 
40.68 
45.06 

49.24 


64.07 
' 


73.38 
76.18 

8i-37 
83-79 


116.92 


"9-99 
120.97 
121.92 


124.62 


5.32 


4'57 


^.00 


3-43 
3.26 


2.66 
2.53 


90.39 
92.40 
94-32 
96.16 

97-93 
99-63 

101.26 
102.83 
104.34 

105.79 
107.20 

108.56 
109.87 
111.14 

113-55 


1.36 


i. 09 
1.05 

I.OO 

0.98 

0.95 
0.92 


128.72 
129.49 
130.24 
130.98 
131.70 

132.41 


°-77 
°-7S 
°-74 

°-72 
0.71 


O.OO 


5.27 


37-52 

42.22 


- 


69.28 


80.79 

83.31 
85.71 
88.00 
90.18 
92.25 

96.14 

97-95 

99.70 

101.37 

102.97 
104.52 
106.00 

108.81 

110.14 
111.43 
112.68 
113.88 
"5-05 
116.18 

118.34 
H9-37 


2.29 

2.18 

2.07 
1.99 

1.90 
I.8i 
1-75 


T  ?  C 

' 


1.33 


121.36 

122.31 

123.24 


129.89 
130.64 

132.09 
132.80 

133-49 


°-95 
°-93 


... 
°'7S 


0 


0.69 


0 

1 

2 
3 
4 

5 
6 
7 
8 
9 

10 
11 
12 
13 
14 

15 
16 
17 
18 
19 

20 
21 
22 
23 
24 

25 

26 
27 
28 
29 

30 
31 
32 
33 
34 

35 
36 
37 
38 
39 

40 
41 
42 
43 

44 

45 
46 

47 
48 
49 

50 
51 
52 
53 
54 

55 
56 
57 
58 
59 

60 


TABLES    FOR    THE    TRUE    ANOMALY. 


29 


M 


«  =  -57 


-58 


=  -59 


.60 


e  =  .61 


.62 


.V 


60 
61 
62 
63 
64 

65 
66 
67 
68 
69 

70 
71 
72 
73 
74 

75 
76 
77 
78 
79 

80 
81 
82 
83 
84 

85 

86 
87 
88 
89 

90 
91 
92 
93 
94 

95 

96 
97 
98 
99 

100 
101 
102 
103 
104 

105 
106 
107 
108 
109 

110 
111 
112 
113 
114 

115 
116 
117 
118 
119 

120 


12688 

32 

129.16  °-7S 

129.89 

* 


A 

°"> 


0.73 
0.72 


'3^32  - 
.32.01 

IE-S  oil 

0.66 


.32-69 
133-37 


M 


.38.40 
.38-99   ° 
.39-57    OS7 
140.14 
140.71    °-" 
141.27   °'56 
141.82   °-55 

142-37  °;" 
142.91 
.43.44  °'53 

'43-97  °'*3 
.44-49  °'S 

145.00      5 
*°        0.51 


146.52 

47.61 

'47.50 


148:94  °-48 
.49-4.  ° 
149.87  °-4° 
0.46 

.50.33 
.50.79  ° 

'5.-24 
I5.-4  °'45 
.52.14  * 


153-45  ° 
153.88  °-43 

'54-3' 


155-58 
'55-99 
156.41 

156.82 
.57-22 

I57-63 
.58.03 

158.43 
.58.83 


:•  :: 

°'4 


0.41 


I2800 

'28-76 
129.50 

'3-3 

'3°-95 


, 


II 

'37-50  o;6o 

.38.10 
138.70  ° 
.39-28 
.39-86     ' 


°'S4 


-»• 

O.SI 


14*9 

142.63 

'43-7 


.44-73 

.45-24 : 

.45-75   o'.jo 

146.25 
146.74  °-4° 


*  0.47 
148.66 
149-13  °'4! 

Is  a 


150.96 
151-4. 

152.29 
152.73 

I53-.6 
.53-59 


'54-86 


'57-31 


158.88 
I59-27 


0.39 


129.12 
129.86  °-74 

'3-59 


132.00 

'33-37 
134.04 


0.69 


'35-34 


137-82 
138.42 

.39-00 
.39-59 


'4-8 


142.91 

143-44 
I43-96 

144.48 
144.99 

.45-49 

•45-99  0 
146.48  °'49 

146.97 
147-45 
.47-93 
148.40 
148.87 

.49-33 
.49-79 


„ 


0.49 


0.46 


-       0.4 


150.70 


152.02 

152.89 
.53-3. 

.53-74 
I54-.5 
.54-57 
I54-98 
.55-39 


°'44 
0.44 


157-40 

.57-79 
158.18 

158.57 

158.95 
'59-34 

I59-72 


0.4t 


0.39 
0.39 

0.38 
0.39 
0.38 


.33-05 

.33-72 
134-38 


3 


'39-32 


.-02 


142.66 

is;? 


_T  0.49 

jjrja  0.48 

4'"   0.48 
147.69 
,7s  TA  °-47 


149.09 
.49-55 
150.00 

.50.89 
I5I.33 


152.20 


'53-47  : 
.53-89  0'4* 


'54-30 

i 


0.41 

0.41 
0.41 
0.41 
0.40 
0.39 


I59-78 
160.15 


.34-74 


154.87 


0.6s 


137-88 
138-48 
I39-07 
I39-65 
140.22 

140.78 
141.88 


.43-48 
144.00 

144-51 
145.02 

I45-52 
146.01 


0.57 
0.56 


* 


146.98 
147.46 
.47-93 
148.40 
148.86 
.49-32 
.49-77 

150.66 
151.10 


°'44 


.52-81 


0.40 
0.41 

0.40 


.58.37  °;38 

'58-75  o  37 
'59-'2  o  37 
.59-49  „ 
159.86  J 

.60.23  °'3I 
0  0.36 

160.59 


.33-79 
.34-45 
135-1. 

.35-76 
.36-39 
137.01 

.37-63 
.38-23 

138.82 
139-4. 
.39-98 
140.55 
141.11 

141.66 

142.74 
143.26 
.43-79 
144.30 
144.81 

I45-3I 
145.80 
146.29 


0.62 
0.60 

0.59 
0.59 


0 

so 
O.SS 


o 


147-72 

1S8 


150.00 


.58-48 
158.85 

159.22 
159.58 


- 


160.66   °-3S 
0.36 

161.02 


0.47 
0.46 
0.45 

0.45 

0.44 


.53-00 
153-42    o"^ 

itl  21    °'4° 
'54^3    *£ 

•55-03  :;4: 

.55-43  „  ,0 
•55-82 
156.21  ^jg 


•33°49  0^8 

ii 

liS  - 


I39.76 


IJSS 

46.09 


2 


148.91 

'49-36 


152:31 

'5-79 


154.01 
I54-4I 


.55-59 


0.40 
0.40 


O. 


0.37 

0.37 
0.36 

158.97   °'37 
.59-33 

•    I59-69   „ 
160.04          f 

;  160.40  °-36 
1  Kl »:« 

0.34 
I   161.44 


60 
61 
62 
63 
64 

65 
66 
67 
68 
69 

70 
71 
72 
73 
74 

75 
76 
77 
78 
79 

80 
81 
82 
83 
84 

85 
86 
87 
88 
89 

90 
91 
92 
93 
94 

95 
96 
97 
98 
99 

100 
101 
102 
103 
104 

105 
106 
107 
108 
109 

110 
111 
112 
113 
114 

115 
116 
117 
118 
119 

120 


3° 


TABLES    FOR    THE    TRUE    ANOMALY. 


M 


-57 


120 
121 
122 
123 
124 

125 
126 
127 
128 
129 

130 
131 
132 
133 
134 

135 
136 
137 
138 
139 

140 
141 
142 
143 
144 

145 
146 
147 
148 
149 

150 
151 
152 
153 
154 

155 
156 
157 
158 
159 

160 
161 
162 
163 
164 

165 
166 
167 
168 
169 

170 
171 
172 
173 
174 

175 
176 
177 
178 
179 

180 


159-22  """ 

159.61  39 
160.00  °"39 

160.39  °'39 

y    0.39 
160.78 

-t, ',,    0.38 


»•" 


0  „ 
°'37 

3 


163.42 
163.79 

164.52 
164.89 

I65.25 
165.61 

165.98 

166.34 
166.69 
167.05 
167.41 
167.76 

I68.I  I 
168.47 
168.82 


169.86 
I7O.2I 
170.56 
170.90 
171.24 

I7L59 
I7L93 
172.27 
I72.6I 


0.35 

0.36 
0.35 


°'3S 


°-34 

0.3S 


0.34 
0.34 
0.34 

*'"vo    0.34 

I73.29   „  ,. 

173.63    °'34 

173.97 

I74-3I 

I74-65 

174.98 

Ultt  o-34 
175-99  °'33 
176.33  03l 
176.66 


0.34 
0.34 
0.34 
0.33 

0.34 


0.34 
0.33 


177.00 

'77-33  0  , 
177.67  °'34 
178.00  °'33 

0.33 
178.33 
178.67 
179.00 

179-33 
179.67 

iSo.OO 


„  7 

°'34 


e  =  .58 


160.80 

161.18 
161.56 

162.30 
162.67 


165.56 
165.92 
166.27 

166.62 
166.97 
167.32 
167.67 
168.02 

168.36 
168.71 
169.05 
169.39 

170.08 
170.42 

170.75 
171.09 

I7L43 

171.76 
172.10 

172.43 
172.77 


0.38 
0.38 


°-37 

0.37 


3 
3 


0.35 


0.34 

0.35 
0.34 


°-34 


0.33 
0.34 


°'33 


173-43 
173-77 
174.10 


0.33 

0.34 
0.33 
0.33 


174-43   „  „ 

17476   °'33 

0.33 

I75-09 
I75-42 
175-75    „  ,. 
176.08    °'33 
176.40    °-32 

176.73 
177.06 

177-39 
I77.7I 
178.04 

178.37 
178.69 
I79.O2 

179-35 
179.67 

iSo.OO 


0  33 

° 

"'" 


0.33 


0.33 


-59 


I6O.O9 

160.47  °'38 
T*  n  -*i 
160.84 

161.21 


161.58 
161.95 
162.32 
162.68 


0.37 
0.37 
0.37 


163.40 

i63-76 

164.11 


°'37 


°-36 


165.87  „ 
166.22   35 

166.56  °'34 
0   0.35 


0.34 
0.34 


°'34 


I67.93 
168.27 

168.61 
168.95  °'34 
I69.28  °'33 
169.62 


170.29 
170.62  °'33 

170.95  ° 
171.28  Q-*" 

0.33 


172.60  °'33 
172.92  °-32 
173-25 


173-57 
173.90 
174.22 

174-55 
174.87 

175-19 
175-52 
175-84 
176.16 
176.48 

176.80 
177.12 

177-44 
177.76 
178.08 

178.40 

179.04 
179-36 
179.68 

180.00 


0.32 

0.33 
0.32 


'.32 


°'3 

°'32 
0.32 


e  —  .60 


160:89  °'37 

161.26  ° 

161.62  °'3^ 
0.36 

161.98 

162.34  °'3 

162.70   3 

-  0.35 


'63-76 
164.11 
164.46 


176.56 

176.87 
177-18 
I77.50 

178.12 

178.44 

178.75 
179.06 

179-37 
179.69 

180.00 


°-3S 
°-34 


166.18 
166.52 
166.85 

167.19 

167.53 
167.86 
168.19 
168.53 

168.86 
169.19 
169.52 
169.84 

170.50 
170.82 


172.76 
I73.07 
173-39 

I737I 
I74-03 
174-35 
174.66 
174.98 


°-33 

0.34 


°'33 


0.32 
0.32 
0.31 


0.31 


0.31 
0.32 


.61 


161.67 


°'36 


162.02    °-35 
0.35 

162  7  *   °'36 

l63-o8  °'3S, 


164.46  °-3s 

16^.80  °'34 
165.14  °'34 


166.48  °-33 

166.81  °"33 


168.13  :-3 
168.45  °-3 


169.10 


0.32 


°'32 


0.32 


169.74 
170.07 
170.39 

170.70 
I7I.O2 

I7I-34 
171.66 
171.97 

172.29 
172.60 
172.91 
I73.23 
173-54 

173.85 
174.16 

174-47 
174.78 

I75-09 

17540 
I75.7I 
176.02  -*• 

'76-32  °03° 

176.63  0;3I 
176.94 
177.25  °'3' 
177-55  „ 
177.86  O6t 

178.47  . 
178.78  °-31 
179-08  ° 


180.00 


0.31 
0.31 
0.31 
0.31 

0.31 


=  .62 


161.02 
161.37 
161.72 
162.07 
162.42 


'63-79 


165.46 

166.12 
166.45 
166.78 
167.10 


168.39 
168.71 
169.03 

169-34 
169.66 
169.97 
170.29 


0.35 
0.35 
0.35 


0.34 
0.33 

0.33 
0.33 
0.33 
0.33 


0.32 
0.31 


0.31 


0.31 
0.31 
170.91 
171.22    ° 

"71-84  °'3! 
172.15 

172.46 
'7-76  -£ 
I73.07  0 
173-38  °03I0 
173-68  „ 


'74-59 


0.30 

'75-5° 
175.80  °-3° 

176.10  °-30 
"76.40  °-3° 
176.71 

177.01 

177-31 
177.61 
177.91 
178.21 


0.0 


0.30 
0.30 

0.29 


179.70 
180.00 


0.30 


JW 


0.34 
0.34 


161.44 

161.79  °'3S 

162.13  °'34 
.62.47  !"34 
162.81 

163-15  0 

I63'49  o'3.4 

163.82  °'33 

164.15  °'33 

164-48  °'33 

0.33 
164.81 

165.14  °'33 
165-47  ° 

"65-79  „':: 

166.11 


166.43 

166.75 
167.07 

167-39 


0.32 

0.32 

0.32 
0.31 


0.31 
0.31 


168.65 
168.96 
169.27 

169.58 
169.89 
170.20 
170.50 
170.81 


172.02  ° 

0.30 
172.62 

172.92  °-3° 

173.22  °'3° 
I73.52  '3 

"73-82  °'3° 


!?K!  £ 

1 75-3 1  „ 


176.49  0 
'76.78  °' 


177.66  °'29 
'77-95  „ 
"78-25  °-3° 


179.71 
180.00 


0.29 


120 
121 
122 
123 
124 

125 
126 
127 
128 
129 

130 
131 
132 
133 
134 

135 
136 
137 
138 
139 

140 
141 
142 
143 
144 

145 
146 
147 
148 
149 

150 
151 
152 
153 
154 

155 
156 
157 
158 
159 

160 
161 
162 
163 
164 

165 
166 
167 
168 
169 

170 
171 
172 
173 
174 

175 
176 
177 
178 
179 

180 


TABLES    FOR    THE    TRUE    ANOMALY. 


.65 


e  =  .66 


e  =  .67 


«  =  .68 


e  =  .69 


.70 


M 


0 

1 

2 
3 

4 

5 
6 
7 
8 
9 

10 
11 
12 
13 
14 

15 
16 
17 
18 
19 

20 
21 
22 
23 

24 

25 
26 
27 
28 
29 

30 
31 
32 
33 
34 

35 
36 
37 
38 
39 

40 
41 
42 
43 
44 

45 
46 
47 
48 
49 

50 
51 
52 
53 
54 

55 
56 
57 
58 
59 

60 


o.oo 

5-92 

11.79 


I'll 
'8 


28.68 


5-47 


43.83 
48.43 

52-78 
56.91 
60.8, 


fflr*  3-29 
71.28 

-4-4°  *" 

&%  >? 

82.78  I'6* 


89-93 
92.08 

96.10 

97-97 

99-76 

101.47 

103.12 

,04.70 
,06.21 
,07.67 
109.08 
110.43 

,13.00 
114.22 
115.40 
116.54 

,17.65 
1,8.72 

120.77 
121-75 

122.7, 
123.64 


-71 

•6s 

•  S8 

•  SI 


.26 

.22 

.18 


I26'29 


0.96 


0.84 


•»•*> 


::: 


O.OO 

6.19 

12.33 
18.36 

24-23 

29-91 
35-36 


6.14 
6.03 
S-87 
5.68 

5-45 


45-53 


StS 

62.81 


73-34  ,  .. 
76-45  3 
79-39 


96.04 

97-97 
99-81 

103.26 
104.87 

106.42 
107-91 
109-34 
1,0.72 
1,2.05 

113-33 
114.56 

115-75 
,16.90 
,18.02 


'33-6 


2.03 
1.93 

1.84 
1.76 


I-SS 


1.38 
1.33 
1.28 

1.23 


,c    I-I9 
I. IS 


122.16 
123-12 


-7-56 


129.96 


0.94 


0.72 

0.70 

; 


O.OO 

6.49 

I2.9I 

19.21 

31.22 
36.86 
42.23 


4.52 


60.88 
64-87 

68.6, 
72.13 

75-44 
78-55 
81.48 
84.24 
86.85 

91.64 
93-85 
95-95 
97-95 

i  99-85 
!  101.66 

i  103-39 
|  105.05 
|  106.63 

108.15 
,09.61 

!  ill. 01 

112.36 

'  ,13.66 

114.91 

1,6.12 

,17.29 

!  118.41 
II9-5I 
120.56 
121.59 
122.58 

124.49 


128.81 


3-31 

3.II 
2.93 


2.46 


134-57 


135-64 


•  58 

•S2 


u 


0.81 
0.78 


130.40 
,31.16 
,31.9, 
132.64  °'73 

133-35 


°'7S 


0.71 


136.70 


O.OO 

6.81 
13-53 

26.49 
32.61 


s'21 
54-09  *'jg 

58.67 
62.97  4"30 
67.60  4'°3 

7°'76  I'll 

74.29  *•*• 

*  3.30 

77-59  .  I0 
80.69  3'10 
83-60  2'9' 

86.34  I'" 
88.92  2'58 

2.44 


95-84 
97-91 
99.87 

101.74 
103.52 
105.22 
,06.85 
108.40 

109.89 

1,2.68 
114.00 
II5-27 

116.49 
117.68 
1,8.82 
1 ,9.92 

I22.O2 


& 


0 


78 


:  • 


;- 


.19 
•  14 
.10 


0.80 
0.78 

0.74 


133-79 
134-49 


I37-I3 

137-75 


O.OO 


45-81 
51-15 

60.80 

65-15 
69.20 

72.97 
76.50 

79-79 

82.87 


91-03 

93-43 
95-70 
9785 


3-29 


101.81 
103.64 

105-39 
107.05 
108.64 
1,0.16 

111.62 
1,3.0, 

"4-35 
1,5.64 
,16.88 

1 1 8.08 
119.23 
120.34 

,22.46 


1.27 

.83 
.75 

.46 

•39 
•  34 


•  IS 
.II 


ss  :i; 

,27.20 

0.86 
128.06 
,28.9,    ° 


'33-54 


I35.62 

i   ,36.28 

136.93 

137-57 

!  138.80 


o.oo 

7.51 
14-93 


A 

7.51 
7.42 

7.21 


5- 


63.01 


3.28 


75-24 
78.76 

82.04 

87^96 
90.64 


SS  :•;; 


-.'i 

••••, 
It 
tt 

4  = 

n 


M 

"5 


,24.91 
,25.86  °-9S 
,26.78  °''2 
127.67  °'89 


s 

0.74 


0.71 
O.69 

0.66 
0.64 


105-55 
,07.26 
,08.89 
1,0.44 

1 1 1-93 

H3-35 
,14.72 
,16.02 
1,7.28 
,18.49 

,19.66 
,20.78 
,21.86 
122.91 


131-01 
131-79 

I33-29 
134-01 
134-72 


137-39 
138.02 

138.64 
I39-25 

I39-84 


0.00 


23.27 
v>  so 

•*   ° 


S 

7  21 

6.86 


3.25 


IS 


101.90 
,03.86 


109.14 
1,0.73 
,12.25 
,13-70 

1,5.08 
1,6.41 
1,7.69 
1,8.92 
120.09 

121.23 
122.32 
123-38 
,24.40 

126.34 
128.17 


'33-78 


.85 
.76 

.67 


•  38 

•  33 


I  ; 


°-87 


'34-50 

i 


0.71 

0.68 
0.68 
o.6s 
0.64 

137-86 

138-49  ** 

139-11 

139-71 


,40.88 


0 

1 

2 
3 

4 

5 
6 
7 
8 
9 

10 
11 
12 
13 
14 

15 
16 
17 
18 
19 

20 
21 
22 
23 
24 

25 
26 
27 
28 
29 

30 
31 
32 
33 
34 

35 
36 
37 
38 
39 

40 
41 
42 
43 
44 

45 
46 
47 
48 
49 

50 
51 
52 
53 
54 

55 
56 
57 
58 
59 

60 


TABLES    FOR    THE    TRUE    ANOMALY. 


M 


e  =  .64 


e  =  .66 


.68 


.70 


M 


60 
61 
62 
63 
64 

65 
66 
67 
68 
69 

70 
71 
72 
73 
74 

75 
76 
77 
78 
79 

80 
81 
82 
83 
84 

85 

86 
87 
88 
89 

90 
91 
92 
93 
94 

95 
96 
97 
98 
99 

100 
101 
102 
103 
104 

105 
106 
107 
108 
109 

110 
111 
112 
113 
114 

115 
116 
117 
118 
119 

120 


60 
61 
62 
63 
64 

65 
66 
67 
68 
69 

70 
71 
72 
73 
74 

75 
76 
77 
78 
79 

80 
81 
82 
83 
84 

85 
86 
87 
88 
89 

90 
91 
92 
93 
94 

95 
96 
97 
98 
99 

100 
101 
102 
103 
104 

105 
106 
107 
108 
109 

110 
111 
112 
113 
114 

115 
116 
117 
118 
119 

120 


135-88  *• 


'39-55  El 
140.12 

0.57 
140.69 

.41.25  °'5' 
141.80  5S 

.42.34  "•" 
142.87  °;*3 

'43-39  0 
143-9.  'I, 


145.42  ^r 

.45-9.  „ 
.46-39  °-4! 
146.87  °-48 

.47-34  °'47 
147.81 


\j,t}\j 

148.27 
148.73  °'46 
149.18  °'4S 
149.62  °'44 
150.06  °'44 

0.43 

150.49  „ 
150.92  °'43 

151.35  °'43 

j^f :::: 
152.60 

'53-01  °-4' 


154.61 
155.00 

155-39 
155-77 


.57.27  °'37 

.57.64  °'37 

158.0,  °;37 

158.37  ,6 

158.73  °'3* 

159.09  °-3° 

159-45  ° 

159.80  J5 

0.35 

160.15 

160.50  °-35 

160.84  °-34 

161.19  °'3S 

161.53  °-3J 
161.87 


183  •? 

S5  s 

.38.75 
.39.35 
.39.93 


;: 

" 


*« 

°-s4 


143.22 
143.74 
.44.25 


.45.74 

146.71 

147.18 


0  „ 
°'SI 


°-47 


149.01 

.49.45  ° 
149.89  • 

.50.33  °;44 

151.18 
151.60  °-42 
152.02 

.52.43 
152.84 


°'42 


• 


154.8. 

.55-20 
155-58 


0.39 


156.70 


SS 


'59.57  rn 

.59-92 

160.26 

0.35 

160.61 

160.95  °'34 

,61.28  °'33 
161.62  °'34 
.61.95  °'33 

3  0.33 
162.28 


136.70 
'37-33 


.39-74 
140.32 
140.88 
141.44 
141.99 

143.06 
.43-58 
144.09 
144.60 

145.10 

.45-59 
146.08 


. 

-  3 


0  ,.„ 

3 

°'s6 


0.51 
0.50 

0.49 


o  s 

°-45 

148.86  °-45 

'49-31  - 


148.41 


'50-61 


151.86 


0.42 
0.42 
0.41 

0.41 


II 5 

.55-03      ',« 

.55.4.  o;37 
j  55-78  037 

iseisf  °-37 

£    O  O.37 

^       '_£      0.36 

O.36 


0.34 
0.34 


.59-37 
I59.7I 
160.05 

.60.39  °'34 

160.73       J4 

J    0.33 

161.06 

.61.39  ^33 
161.72  °'33 
162.05  °'33 
162.38  ° 

162.70 


140.72 
141.28 
141.83 


0.57 
0.56 

0.55 


145.46 

.45-94 
.46-43 
146.90 


153-33 


°'47 


148.28 

'48-73  0 


150.05  Q" 
150.47 


.  ., 


.51.73  r 
152.14 


0.40 


„ 

2 


156.00 

156.36 
.56.73 
.57-09 


7 


0.35 


159.86 

160.20  °'34 

ifeii  - 
'6--'9 ::?, 
161.51 

161.84  °-33 

162.16  °-32 

162.48  °-32 

162.80  °-32 
0.31 
163.11 


1  388o 
13940 
139-99 
'40-57 


142.24 
'42'77 


H4-34 


146.31 
146.78 


0.55 
0.53 
0.53 
0.52 
0.52 

0.50 


0.47 


148. 17 

148.62  °-4s 
0.44 

149.06 
149.50  °-44 

.49.93  :i3 
.50.36  ° 

150.78  °-42 
0.42 

151.20 
151.61  °-41 
152.02  4 
.52.42  °-4° 

152.82  °-4° 
0.39 


.53-99 
.54-37 
.54-75 

.55-12 
.55-49 
.55-86 
156.22 
156.58 


°'37 


.57.64  "3* 

.57-99  „ ,; 
.58.34  034 
158.68 
159.02  °-34 

IW-36  °'34 

159-69     '" 

160.02  °-33 

0.33 

160^68  °'33 
161.00  °'32 
161.32  °'32 

161.64  °'32 
'  0.32 

161.96 
162.28  °'32 
162.59  °'31 

162.90  °-3; 
163.21 


.39.84 
140.43 
141.00 
.41.56  °-s6 

r     •*       nee 
142.11 

142.66 
.43.I9 
.43-7. 


°-ss 

0.55 


'44-73  0;;!0 

1C    -70  °'49 

8S  °'4' 

,46.68  °-47 


'48-52  «•« 
°-4s 


150.68  °-4 


1*21,2    °'40 
152.71    °"39 

'»»    ^38 

'53-49  :;3: 

.  53-88 
.54-26  °'38 
I54-63    '„ 
.55-00    ••" 

.55-37  0;j7 

'55-74  o;36 
156.10 

.56.46  °-3! 


158.20  °-34 

.58.54  „' 
158.87  °-33 

.59-21 
.59-54  „' 


.63.52 


0.31 


160.84 
,6147  °-32 

'62'-'0  o^ 
162.41 
162.72  3t 

163.02  °-30 

:§:§  3 

.63-93 


140.88 

.41-45 
,42.00 

142-55 
143-09 

143-62 

.44.13 
,44.64 

145-15 
.45-64 


* 


°-SI 

°'SI 

- 


0.45 


,47.07 
.47-54 
.47-99 
,48.44 
,48.89  °'4S 

'49-33  ° 
149.76 
150.18  ° 

150.60 
,51.02  °'42 
•51.43  °'4' 


.53-4. 
153.79 
I54.I7 

.54-54 
.54-91 


0.35 


.57.05 


158.08 

158.41  °-33 

j^g  £5  0.34 

I59!o8  °'33 

'59.4.  - 


i^T1  °'32 
160.69   32 

,61.01  °'32 
0.31 

161.32 
161.63  °'31 
,61.94  °'31 
,62.24  °'3° 
I62'55  o^o 

,62.85 
.63.15  °'3" 
.63.45  ° 

!§:2{  - 

0.29 

.64.33 


TABLES    FOR    THE    TRUE    ANOMALY. 


33 


M 


e  =  .64 


120 
121 
122 
123 
124 

125 
126 
127 
128 
129 

130 
131 
132 
133 
134 

135 
136 
137 
138 
139 

140 
141 
142 
143 
144 

145 
146 
147 
148 
149 

150 
151 
152 
153 
154 

155 
156 
157 
158 
159 

160 
161 
162 
163 
164 

165 
166 
167 
168 
169 

170 
171 

172 
173 
174 

175 
176 
177 
178 
179 

180 


161.87 
162.20 
162.54 
162.87 
163.20 

163.53 
163.86 
164.19 


0.33 
0.34 
0.33 
0.33 
0.33 

0.33 


165.80 

I66.ii 


167.37 
167.68 
167.99 

168.29 
168.60 
168.91 
169.21 


0.30 


°-3° 


17042    °'3° 

170-72    °'3° 
I7I.O2 

I7I.3I 
I7I.6I 


°-3° 

0.29 


172.20 

'7-50 


si 

I  1  A     CA      O.29 

,-,.  e,   °-29 


'75-70 


177.14 


178.00 
178.28 


179.71 

180.00 


e  =  .65 


*• 


0.29 


°-28 


°-29 
°-28 


I6228 

162.61  °'33 

162.94  °'33 

°'33 


°-32 


164.87  °-3 


165.81 
166.12  ° 

166.43   ° 

167.05   Q  3Q 

167.66  °'31 
167.96  °'3° 

168.26  °'3° 
0.30 

168.56 
168.86  0'3° 
169.16  °'30 

'69.46  °:3° 


«• 

°-3° 
°-29 


0.29 


.66 


170.64 

170.93 
171.22 


172.09  " 

'72-38  HI 

'72-67  0;29 

T»«  «.  o. 28 


0.29 
0.28 


'75-52  — 
175-80 
'76-08  °;28 

..28 


177.20 


178.60 
178.88 
179.16 
179.44 
179.72 

180.00 


••*! 

-2 


162.70 
163.02  °'32 

i63-34  :-3: 

163.66  °'32 
163.98  °'32 


0.31 


164.91 
165.22 


166.45  °-31 
166.75  °-3° 


167.95  °-3 
168.24  °-2 


170.28 


'73-'2  0.28 
|73-40  0  28 

I73-96  °'ll 

174-24  0;27 
174-51  0 

J74-79  „',„ 
175-07 
175-35 
175-62 


•* 


175.90 

'76-'7 
'76-45 


"'28 
" 


'77-27 


178.09 
178.36 

178.64 
178.91 
179.18 
179-45 
179-73 
180.00 


°'27 


0.31 

164.36  °'31 
"  °     0.30 

164.66 
164.97  ° 

si 

166.17 


167.06 


168.23 
168.52 

169.09 
169.38 


171.91 

' 


°-29 


e  =  .68 


0.28 
0.28 


0.28 
0.28 

0.27 


'73-01 


174.37 

174.65 
174.92 

175.19 
175.46 
175.73 

175.99 
176.26 

176.53 
176.80 
177.07 


27 


0  „ 
°'27 


'78-94  He 
179.20  ' 

'79-47  0H 
'79-73  0.2? 
180.00 


l66-5'  o  20 
166.80    '  • 

167.09  °'29 

167.38  I'll 

167.95  - 
168.23  °-28 

I68'52  oil 
168.80  °'28 

169.08  °'28 
0.28 


0.28 
0.27 
0.28 


170.74 

171*1  °-*l 
171.29  °'28 
171.56  °'27 

171.83  °'27 
0 


172.10 


172.9 

'73-8 


0.27 
0.27 


°-27 


173.98 
174.24 

174.51 

174-77 
I75-04 


176.09 

176.35 
176.62 
176.88 


177.92 
178.18 

'78-44 


180.00 


.69 


sts  £ 

164.82 
165.11  °'29 

0.29 

165.40  „ 


166.27  °'29 


168.24 


0.27 

169.62 

169.89  °-27 
170.16  °-27 

170.43  ° 
170.70  0;27 

170.97  0  27 

171.24       ' 

111 


'73-35 


174-39  „ 
174.64  °-2 

*  0.2 


T2  0.26 

1.26 


"2 
°'26 


0.25 

177.97  I'll 

0.25 


'79-4  :; 

'79-49  °' 
'79-75 


175-93  I 
176.70 


e  =  .70 


Af 


180.00 


164.91  °-2 


!S3?  - 


ii 


168.54 
168.8?  °'27 
169.08  °'27 

'^9-35  °0H 

169.61  °'26 

0.27 

169.88 
170-14  °'2, 


'70-93 


1-2  7? 

173:- 
173-26 

'73-5! 


0.26 
0.26 
0.26 

0.25 
0.26 
0.26 


,-.    ,_ 


0.2S 


0.2S 


'75-53  °0H 
175.78  °'2S 
176.03  °'2S 

176.28 

176.53 
176.78 

177.03 

177-28 

177-53 
177-77 
178.02 
178.27 
178.52  °'2S 

178.76 
179.01 
179-26  °'2S 
179.51  ° 

179-75  0; 2S 
180.00 


0.2S 


0.2S 


°'2S 


0.24 

0.2S 


120 
121 
122 
123 
124 

125 
126 
127 
128 
129 

130 
131 
132 
133 
134 

135 
136 
137 
138 
139 

140 
141 
142 
143 
144 

145 
146 
147 
148 
149 

150 
151 
152 
153 
154 

155 
156 
157 
158 
159 

160 
161 
162 
163 
164 

165 
166 
167 
168 
169 

170 
171 
172 
173 
174 

175 
176 
177 
178 
179 

180 


34 


TABLES    FOR    THE    TRUE    ANOMALY. 


M 


e  =  .71 


.72 


.73 


e  =  .74 


-75 


.76 


.77 


M 


0 

1 

2 
3 

4 

5 
6 
7 
8 
9 

10 
11 
12 
13 
14 

15 
16 
17 
18 
19 

20 
21 
22 
23 
24 

25 
26 
27 
28 
29 

30 
31 
32 
33 
34 

35 
36 
37 
38 
39 

40 
41 
42 
43 
44 

45 
46 
47 
48 
49 

50 
51 
52 
53 
54 

55 
56 
57 
58 
59 

60 


o.oo 
8-35 


32.04 

* 


7.94 

7.12 
6.65 


62.88  5-23 

4.81 

67.69 

72.12  4'43 

76.20  4'08 

79-96  I'll 


86.67 
89.66 


99-77 
101.92 

103-95 
105.86 
107.67 

109.39 
1 1 1. 02 
"2-57 
114-05 
115-47 
116.82 
n8.il 

119-35 
120.55 
121.70 

122.80 
123.86 
124.89 
125.89 
126.84  °'9S 

0.94 


2.IS 

2.03 

.91 

.72 

63 

55 
,.|8 


29 


33 


'32'02  o  78 
132.80  °'78 

'33-55  I'" 
I34-29  •'* 


140.19 

'40-77 


141.91 


A 

8.82 
8.65 
8.33 
7.90 
7-39 


0.00 

8.82 

17-47 

33-70 
41.09 

6O.O2 


70.16 
74.60  4'44 

78.67  4'°7 

W ••>  A  T  *5*  /4 
02.41 

85-85  3'44 


2'39 
2.24 


91.99 

94-74 
97.29 
99.68 

101.92 
104.02 
106.00 
107.87 
109.64 

111.31 
112.90 
114.42 
115.86 
117-23 


I2I.O2 
122.18 


.21 
.16 


.03 

.00 
0.97 

'28'30  ™ 

!2?'2°  0.88 
0.84 
0.83 


125.40 
126.40 
127.37 


I34.8I 
135-53 
136.23 

136.91 

ss  °r 
138.86  *** 

139.48  °-°2 
0.60 

140.08 
140.68 
141.26 


0.72 
0.70 

0.68 
0.67 


°'6° 
°'s8 


O.OO 

9-35  9 

i8.48 9-;3 

27'23  I'" 
35-48  *£ 

43-14 
50.19 
56.64 
62.51 
67.86 

72.71 

77-15 
81.20 
84.90 
88.31 


7.05 
6.45 
5.87 

4.85 

4-44 
3-70 


99-56 
101.89 

104.08 
106.14 
IO8.O7 
109.89 
III.6I 

113.24 
1 14.79 
II6.26 
117.66 
Iig.OO 

120.28 
121.50 
122.68 

123.80 
124.89 

125.93 
126.93 
127.90 

128.84  °-94 
129-75  °'ll 


2.19 
2.06 


.63 
.55 


.34 

JK 


12 

09 

1.04 

0.97 


I33.87 

I34.62 
I35.36 
136.07 


°-74 


138.11 

139.38 
I40.OO 

140.60 

0.59 
141.19 
4l.76    »'" 


142.93 


142.88 
I4342 

H3.95 


0.00 

9.91 

19.57 
28.78 

37.40 

45-34 
52-59 
59.16 
65.11 


75-35 

79-77 


133.66 
134-44 
I35-I9 

I35-92 
136.63 
137-32 
138.00 

139-30 
139-92 


9.66 
9.21 
8.62 
7-94 
7.25 


. 
4'4 


9O.8I 

93-90 
96.75 

99-39 


106.26 
108.26 
110.14 
111.91 
H3-59 

115-17 
116.68 
118.10 
119.47 
120.77 

I22.OI 
123.19 
124-33 
125-43 
126.48 

127.49 
128.46 
129.40 


3.09 

2.8S 

2.64 
2.45 

2.14 
.88 


142.29 
142.84 
143-39 
143-93 
144-45 

144-97 


°-97 
°-94 


0.78 
0.75 
0.73 

0.71 
0.69 
0.68 


£ 


°'ss 

0 
° 


O.OO 

10-53" 
20.77 


47.68 


10.53 
10.24 
9.70 
8.99 
8.22 

7-44 


78.07 
82.46  4'39 
86.43 
90.05 


96.38 

99-17 

101.75 

104-14 


3'97 
3'62 
3-30 

3.03 


108.44 
1 10.39 
112.22 
113-94 

"5-57 
117.10 
118.56 

119-95 
121.27 

123-73 
124.88 

125-99 
127-05 
128.06 

129.05 
129.99 
130.90 


g, 
l'*3 


.  -. 
1>IS 


0.99 

0.94 


135-02  "": 

'35-78  °-7° 
'36-50  ^ 
137.21 
'37-90  °of 
138.57  6l 
139.23  'fi. 
139.86  °'63 

O.02 

'4°-48  0.6I 
141-09  ° 


142.26 
142-83 

143.38 
I43-92 
144-45 
144-97 
145.48 

145.98 


°'S7 
0.55 


»;» 


o.oo 


22.08  I 

32.301 

4--70 


ill 


n: 


64.60  6-7 


76.04 

80.88 
85.22 

92.69 
95-92 

98.89 
101.61 
104.12 
106.45 
108.62 


114.30 
115.97 
117.55 
119.04 
120.45 
121.79 
123.07 
124.29 

125.46 
126.57 

128^66 


132.39 
133.24 
134-07 

134-86 


4'34 


2'72 
2'SI 


;•  9 


1.17 


0.73 
0.70 
0.69 

0.67 
0.64 


141.67 

142.83 
143-39 
143-93 
144.47 
144.99 


a 


O.OO 


11.98 


'37-02 


52.87 

60.65 
67.51 

73-57 
83-75 


95-37  3 


104.07 
106.52 
108.78 
110.88 

112.84 
114.67 
116.39 
118.00 


120.97 
122.34 
123.64 
124.87 
126.05 

127.18 
128.26 
129.29 

131-23 
132.15 


26S 

2 


1.96 


1.37 

1.18 
1. 13 

1. 08 
1.03 

0.92 

0.88 
0.85 
0.82 

0.75 
0.72 


146.51 
146.99 


141.06 

141.67  °" 

142.26  °-59 
0.59 

0.56 

'44;5i  0'*4 

145-04  OS2 

145.56 

146.07  °'SI 

146.56  °-49 
I47.05 

'47-53  o;47 
148.00 


0 

1 
2 
3 
4 

5 
6 
7 
8 
9 

10 
11 
12 
13 
14 

15 
16 
17 
18 
19 

20 
21 
22 
23 
24 

25 
26 
27 
28 
29 

30 
31 
32 
33 
34 

35 

36 
37 
38 
39 

40 
41 
42 
43 
44 

45 

46 
47 
48 
49 

50 
51 
52 
53 
54 

55 
56 
57 
58 
59 

60 


TABLES    FOR    THE    TRUE    ANOMALY. 


35 


.71 


.72 


-74 


-75 


.77 


M 


60 
61 
62 
63 
64 

65 
66 
67 
68 
69 

70 
71 
72 
73 
74 

75 
76 
77 
78 
79 

80 
81 
82 
83 
84 

85 
86 
87 
88 
89 

90 
91 
92 
93 
94 

95 
96 
97 
98 
99 

100 
101 
102 
103 
104 

105 
106 
107 
108 
109 

110 
111 
112 
113 
114 

115 
116 
117 
118 
119 


141.91 

143-00 

143-54 
144.06 

144-57 
145-07 


0.51 

0.50 
0.50 


™ 
147.93 


• 


152.17 
152.57 
152.95 

153-34 
I53.72 
154.10 

154-47 
I54-84 


155.92 


0.40 
0.40 
0.40 
0.38 
0.39 


I64-45 


0.34 


3 

° 


0.34 

156.96  „  „ 
I57.30 
157.64 
I57.98 

158.31  ~  33 

158.64 

158.97  : 

159-29  IT 

159-62  " 

159-94  0;3I 

160.25 

.60.57  :~32 

160.88  °'31 

161.19  °'31 

161.49  0'3° 

*  0.31 

161.80 

162.10  °'3° 

162.40  °-30 

162.70  °-3° 

163.00  °'30 

J  0.29 

.63.29 

.63-58  :;29 


120   164.73 


0.29 
0.28 


142.93 
143-47 
144.00 

I44-5I 
145-02 

I45-52 
146.01 
146.49 
146.97 
147-43 
147.89 
148.34 
148.79 

I49.23 
149.66 

150.08 
150.50 
150.92 


152.13 
152.52 
152.91 
153-29 
I53-67 

154-05 


0.50 

0.49 
0.48 


°'43 
0.42 


-  „ 


'43-95 
'44-47 
.44.99 


146.46 

46.94 


I55.I4 
I55-50 

I55.85 
156.20 

156.55 
156.89 

I57.23 

157-57 
I57-90 
158.23 
158.56 
158.88 


159.21 
159-52  ° 
159.84  - 
160.15  °'3 


0.33 


0.32 
0.33 


161.38  °-3° 

161.68  °-30 

161.98  °-3° 

0.29 

.62.27 

.62.57  °-30 

162.86  ° 

163-15  ° 

.63.44  0; 


.64.85 
165.13 


• 


!l-1r  °'46 
H/-87  „  ., 

.48-32 
148.77 


0.45 
0.45 

0.44 


150.07 

'50-49 


-: 


152.88 
I53-27 
I53-64 
154.02 

I54.38 
154-75 


0.38 
0.36 
0.37 
0.36 


I55-8I 
156.16 

156.51 
156-85 
I57.I8 
157.52 
157.85 
158.17 
158.50 
158.82  " 

I59.I4  ° 

159-45  0'33l 

159-76 
160.07 
160.38  °-31 
160.69  °-31 
160.99  °'3° 


.  . 
°'34 


0.32 
0.33 


161.88 
162.17 
162.46 

162.75 
163.04 

163-32 
163.60 
163.88 


°-3° 


°'29 
0.29 


165.26 
165-53 


'4497 
'45-47 
145-97 
'46-46 
'46-94 


. 

i477  n 

148.32  °-45 

148.77  °'4S 
149.21  «•« 

0.43 


152.50 


153-64 
154.01 

154-38 
154-74 
155-09 

155-45 


0  ,. 

: 


156.48 
.56.82 

157-16 
157-49 
157-81 
158.14 
158.46 


°'33 


0.33 


0.32 
1.31 


1.31 


159.09 
15940 
159-71 
160.02   °-J1 
0.30 

160.32 
I6O.62 
160.92    °'3° 
161.22    °'3° 
I6I.5I 

161.80 
162.09 
162.38 
162.66 
162.94 


0.29 


164.05 
I64-33 
164.60 

I  OJ..o7 
I  o^.  I  ^ 

165.40 
165.66 


0.26 


'46-47  ** 


150.09 

°  ~ 


0.42 


153.28  8 


155.10  "•" 

155-45  rr 
155.80  ^ 

156.14 
156.48  °-34 
.56.82  ° 

.57-15  ° 
157-48  ^;33 

157.80 
158.12  °-32 

158.44  °-3l 
158.76  °-3 

159-07  °  3I 

SiS  E 

its  -° 

160.58  °-3° 
°  0.30 

.60.88 

161.17  °-29 

161.46  °-29 

161.75  °'29 

.62.03  i 
j  0.28 

.62.31 

.62.59  °'2! 
162.87 

18:2  -' 
0.27 

163.69 

163.96  °-27 

164.23  ~ 

164.50  °-27 

164.76  °-26 
0.27 

.65.03 
.65.29 

'65-55  in 
.65.81  °-26 
166.06 


146.99 
147.46  °'47 


165.92      i  166.32 


.48.84 

.49.28 
149.71 
150.14 
150.56 
150.97 

151.38 
151.78 
.52.17 


0.44 


148.00  * 
148.45  °-45 
$£  «•« 

149.35 
149.78 

150.2. 
•  150.63 
i  151.04 
i  151-45 

!  151-85 


'53-32 


154-43 
I54-78 

155-14 
155-49 
155-83 
156.17 
156.51 

156.84 
157-17 
157-49 


°3 


159-07 


159-97 
160.27 
160.56 
160.86 
161.14 


°-31 


0.29 

0.28 
0.29 


161.99  °-2? 

162.27  J^g 

162.82 

'63.IO  °'2 


163.90 

164.16 
164.43 
164.69 

I64-95 
165.20 

165.46 
165.71 
165.96 
166.22 
166.46 

.66.71 


°-39 
°-39 


0.34 
0.34 
0.34 
0.33 


'-39 
.53-76 


0.37 


155-54 

182  - 

'56-56  -I 


!  157-53 
157.85 
158.17 
.58.48 
158.79 


0.31 


159-99  !'3' 

160.28  °-29 

0.29 

160.57 
160.86  °-29 
.61.14  °-28 
.61.43  °'29 

.61.70  °-27 
'  0.28 

!SS  °-28 
!Sio - 


0.2S 
0.2S 
O.26 
0.24 
0.25 


163.86 
164.12 
164.38 

164.63 
164.89 
165.14 

165.39 
165.64 

165.89 
166.14 
166.38 
166.62 

166.86 
167.10 


°'2° 


°-26 


0.25 
0.24 
0.24 
0.24 
0.24 


60 
61 
62 
63 
64 

65 
66 
67 
68 
69 

70 
71 
72 
73 
74 

75 
76 
77 
78 
79 

80 
81 
82 
83 
84 

85 
86 
87 
88 
89 

90 
91 
92 
93 
94 

95 
96 
97 
98 
99 

100 
101 
102 
103 
104 


107 
108 
109 

110 
111 
112 
113 
114 

115 
116 
117 
118 
119 

120 


TABLES    FOR    THE    TRUE    ANOMALY. 


M 


.71 


.72 


-73 


«-  -74 


-75 


.76 


.77 


M 


120 
121 
122 
123 
124 

125 
126 
127 
128 
129 

130 
131 
132 
133 
134 

135 
136 
137 
138 
139 

140 
141 
142 
143 
144 

145 
146 
147 
148 
149 

150 
151 
152 
153 
154 

155 
156 
157 
158 
159 

160 
161 
162 
163 
164 

165 
166 
167 
168 
169 

170 
171 
172 
173 
174 

175 
176 
177 
178 
179 

180 


'65-3° 


g 


0.27 

166.13  „ 

I66.4i  °'28 

166.68  °'27 

166.96  °'28 

167.23  °'27 

3  0.27 

167.50 

167.77  ° 

168.04  I 

168.30  °Q167 

168.83  ° 

169.09  °'26 

169.36  °'27 

169.62  °'2^ 

169.88  0>2° 
0.26 


170.39 
170.65 
170.91 


0.26 


171.42 

171.67  °'2* 

!£?g  "• 
'72-43  °0.ii 

'72'68  o  25 
172.93  ° 
173.18  °'25 

'73-43  ° 

173.68  5 
'*   0.24 


174.42  °'2S 
174.66  °'24 
174.91  °-2S 

0.2S 

'75-16 


176  n  °'24 

176.38  0 
176.62  °-24 
176.86  °-24 
177.10  ° 
'77-35  I'H 

177-59  0 
'77-83  °'  4 


178.55  °;24 

178.80 

179-04  °'2' 
179.28 
179-52  °'24 

179-76  °;24 
180.00 


f  5 

" 


°-26 


166.50 
166.76 
167.03  °-27 
167.30  •  7 

l67-56  °'2° 


168.35 
168.61 
168.86 

169.12 
169.38 
169.63 
169.89 
170.14 

170.39 
170.64 
170.89 

I7I-39 
171.64 
171.89 
172.14 


0.26 

0.25 
0.26 

0.26 

0.26 

0.25 


172.87 


0.25 
0.24 


174.08 

'74-32 


°'24 


175.04 
175.28 

Ii^ 


°'24 


176.47 
176.71 
176.94  °'23 

'77-18  °-4 

177.42 


0.', 


IJSM  °'23 
'78-36  ^4 
178.59 


'79-30 


180.00 


0.23 

0.24 

23 


166.06 


°-26 


'oy  0.27 
166.86 

167.12  °'2* 

167.38  °'2^ 

167.64  °'26 

167.89  °'2S 
'  '  0.26 

168.15 

168.40  °'2f 

168.66  °'26 

168.91  °'2S 

169.16  0-2S 
0.25 

169.41 

169.66  °-2s 

169.91  °-2s 

170.16  °-25 

170.40  °-24 

0.25 

170.65 

170.89  °-24 

171.38  °'24 

171.62  °-24 

0.24 

171.86 

172.10  °-24 

172.58  °-24 

172.82  °-24 

0.24 
173.06 
'73-30  o°'24 
173-53  „ 
173-77  ° 
174.00 

174.24 

174-47 
174.71 

174-94 
I75-I7 


0  „ 

I''.3. 
''4 


S*  o"- 

!%g  "' 

'76.33 :- 
176.56 

176.79  °-23 
177.02 

$3  °- 
0.23 


°-23 
' 


178.40  °-23 

178.63  °-23 
0.23 

178.86 
179.09  °-23 

*    0.22 
0.23 

0.23 


17977 
iSO.OO 


165.92 
I66.?8 
166.44 


. 


167.72    ° 
I67.97    - 
168.22    °'2S 
0.25 

168.47 
168.72 
168.97 
169.21 
169.46 


°'2S 


°'24 


0.24 
169.70 
169.94 
l£?I  -4 
170.42 
170.66 

170.90 


°'24 

°'24 
0.24 


171.38 


.24 


0.23 


172.08 
172.32 
172.55 
172.79 
173-02 

I73.25 


0.23 
0.24 

0.24 
0.23 
0.23 


'  0.23 
174.40 
174-62  °'22 

I74.85  °'23 
175.08  ° 

175-31  0;23 

175-53  0 
'75-76  * 
175-98 
176.21 

176.43 
176.66 
176.88 


0.23 

O.22 

0.23 

O.22 


177.55 
177.78 

178.00 

178.22 

178.44 


0.23 


'79-33  2 


iSO.OO 


166.57 
166.82 


°'26 


1 68:06  °-24 
168.31  °0ll 

168.79 
169.03  °'24 

169^51  °-24 

I69-7S  °'24 


170.46  °'24 
170.69  °'23 

170.92  °'23 
0.24 

171.16 

ll\:ll  - 
;?2:oi  -3 

0.23 

0.22 

172.76  °'23 
172.99  °'23 

'73-2'  0;23 

173-44  0 ,. 
173.66 
173.88  °-22 

,',  ,  ,  0.23 


174.99 

/  1  yy 


°-22 

O  22 

0.21 


I'll 


175.66 
175.88  °'22 
I76.O9  °'21 

'76-3'  I'" 
'76-53  0;22 

176.75 
176.97 

I77.I9 

177.62 
177.84 


178.92 
179.14 
179-35 
179-57 
179.78 

180.00 


166.71 
166.96  °'2S 
167.20  °'24 
167.45  °'2S 

167.69  °'24 
'  0.24 

167.93 
168.17  °'24 
168.41  °'24 
168.64  °'23 
168.88  °'24 


169.12 


0.24 


'169.81  °'23 

170.04  °'23 
*  0.23 

170.27 

170.50  °'23 

170.73  °'23 

170.96  °'23 

171.18  °'22 

171.41 
171.64 
171.86 
172.08 
172.30 


0.23 


0.23 


0.22 
O.22 
0.21 


0.22 


172.97 


173.62 

173.84 
174.06 
174.28 
174-49 

I747I 
174.92 


'75-57  2 


176.42  ° 

176.63  ° 

176.84 

177-06  °'22 

I77.27  ° 

17748  ° 

177-69  0;2I 
177.90 

178.11  °-21 

178.32  °-" 


0.21 
0.21 

1/y-3°  0  21 
179.79 

9  0.21 

ISO.OO 


167.10 

I67'58  °-24 
167.82  °'24 
168.05 

168.29 
168.52  °'23 
168.75  °'23 

,.   *  *•'    /\   -»  t 

168.98 
169.21 

169.44 
169.66 
169.89 
I7O.II 
170.34 


O.24 


0.23 

0.23 

0.22 

0.23 

0.22 


171.00  "' 

171.22  °-22 

171.44  °-" 

™  0.22 

171.66 

171.88  °'22 

I72.IO  °'22 

172.31  ° 

172.53  ° 


173-17 


173.81 
174.02 

174-23 
174.44 

174-65 
174.86 

175-07 
175.28 

175-49 
175-70 

175-90 
176.11 
176.32 
176.52 
176.73 
176.94 
177-14 


177.76 

177.96 
178.17 
178.37 
178.57 
178.78 

178.98 
179.19 


O.2I 
O.20 
0.21 
O.2O 


179.80 
iSO.OO 


120 
121 
122 
123 
124 

125 
126 
127 
128 
129 

130 
131 
132 
133 
134 

135 
136 
137 
133 

140 
141 
142 
143 
144 

145 
146 
147 
148 
149 

150 
151 
152 
153 
154 

155 
156 
157 
158 
159 

160 
161 
162 
163 
164 

165 
166 
167 
168 
169 

170 
171 
172 
173 
174 

175 
176 
177 
178 
179 

180 


67083S 


A 


UNIVERSITY  OF  CALIFORNIA  LIBRARY 


UNIVERSITY  OF  CALIFORNIA  LIBRARY 
BERKELEY 

Return  to  desk  from  which  borrowed. 
This  book  is  DUE  on  the  last  date  stamped  below. 


ASTRdNQMY    LIBRARY 


Jyt 


AUG  ^969 


LD  21-100m-ll,'49(B7146sl6)476 


